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Sample records for delayed nonlinear model

  1. Models of the delayed nonlinear Raman response in diatomic gases

    International Nuclear Information System (INIS)

    Palastro, J. P.; Antonsen, T. M. Jr.; Pearson, A.

    2011-01-01

    We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as O 2 and N 2 , and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas' orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.

  2. Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations

    International Nuclear Information System (INIS)

    Kushner, Harold J.

    2012-01-01

    This two-part paper deals with “foundational” issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.

  3. Research on Adaptive Neural Network Control System Based on Nonlinear U-Model with Time-Varying Delay

    Directory of Open Access Journals (Sweden)

    Fengxia Xu

    2014-01-01

    Full Text Available U-model can approximate a large class of smooth nonlinear time-varying delay system to any accuracy by using time-varying delay parameters polynomial. This paper proposes a new approach, namely, U-model approach, to solving the problems of analysis and synthesis for nonlinear systems. Based on the idea of discrete-time U-model with time-varying delay, the identification algorithm of adaptive neural network is given for the nonlinear model. Then, the controller is designed by using the Newton-Raphson formula and the stability analysis is given for the closed-loop nonlinear systems. Finally, illustrative examples are given to show the validity and applicability of the obtained results.

  4. Hopf bifurcation in love dynamical models with nonlinear couples and time delays

    International Nuclear Information System (INIS)

    Liao Xiaofeng; Ran Jiouhong

    2007-01-01

    A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results

  5. Analysis of an Nth-order nonlinear differential-delay equation

    Science.gov (United States)

    Vallée, Réal; Marriott, Christopher

    1989-01-01

    The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.

  6. Nonlinear free vibration control of beams using acceleration delayed-feedback control

    International Nuclear Information System (INIS)

    Alhazza, Khaled A; Alajmi, Mohammed; Masoud, Ziyad N

    2008-01-01

    A single-mode delayed-feedback control strategy is developed to reduce the free vibrations of a flexible beam using a piezoelectric actuator. A nonlinear variational model of the beam based on the von Kàrmàn nonlinear type deformations is considered. Using Galerkin's method, the resulting governing partial differential equations of motion are reduced to a system of nonlinear ordinary differential equations. A linear model using the first mode is derived and is used to characterize the damping produced by the controller as a function of the controller's gain and delay. Three-dimensional figures showing the damping magnitude as a function of the controller gain and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated and compared. To validate the single-mode approximation, numerical simulations are performed using a three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the first-mode vibration

  7. Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence

    Science.gov (United States)

    Zhang, Shou-Peng; Yang, Yun-Rui; Zhou, Yong-Hui

    2018-01-01

    This paper is concerned with traveling waves of a delayed SIR model with nonlocal dispersal and a general nonlinear incidence. The existence and nonexistence of traveling waves of the system are established respectively by Schauder's fixed point theorem and two-sided Laplace transform. It is also shown that the spread speed c is influenced by the dispersal rate of the infected individuals and the delay τ.

  8. Global stability, periodic solutions, and optimal control in a nonlinear differential delay model

    Directory of Open Access Journals (Sweden)

    Anatoli F. Ivanov

    2010-09-01

    Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.

  9. Dynamics of Nonlinear Time-Delay Systems

    CERN Document Server

    Lakshmanan, Muthusamy

    2010-01-01

    Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...

  10. Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

    Science.gov (United States)

    Bache, Morten; Lavrinenko, Andrei V.

    2017-09-01

    Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

  11. Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

    International Nuclear Information System (INIS)

    Kushner, Harold J.

    2012-01-01

    This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

  12. Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

    Science.gov (United States)

    Chunodkar, Apurva A.; Akella, Maruthi R.

    2013-12-01

    This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

  13. Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

    Directory of Open Access Journals (Sweden)

    Chang Che

    2018-01-01

    Full Text Available This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

  14. Stability Analysis of Nonlinear Time–Delayed Systems with Application to Biological Models

    Directory of Open Access Journals (Sweden)

    Kruthika H.A.

    2017-03-01

    Full Text Available In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used in the construction of an appropriate Lyapunov–Krasovskii functional for stability analysis of the networks around an equilibrium point. This analysis translates to verifying equivalent LMI conditions. A delay-independent asymptotic stability of a second-order model of a gene regulatory network, taking into consideration multiple commensurate delays, is established. In the case of cancer immunotherapy, a predator–prey type model is adopted to describe the dynamics with cancer cells and immune cells contributing to the predator–prey population, respectively. A delay-dependent asymptotic stability of the cancer-free equilibrium point is proved. Apart from the system and control point of view, in the case of gene-regulatory networks such stability analysis of dynamics aids mimicking gene networks synthetically using integrated circuits like neurochips learnt from biological neural networks, and in the case of cancer immunotherapy it helps determine the long-term outcome of therapy and thus aids oncologists in deciding upon the right approach.

  15. Controllability of nonlinear delay oscillating systems

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    Chengbin Liang

    2017-05-01

    Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.

  16. Gain scheduling for non-linear time-delay systems using approximated model

    NARCIS (Netherlands)

    Pham, H.T.; Lim, J.T

    2012-01-01

    The authors investigate a regulation problem of non-linear systems driven by an exogenous signal and time-delay in the input. In order to compensate for the input delay, they propose a reduction transformation containing the past information of the control input. Then, by utilising the Euler

  17. Nonlinear Estimation of Discrete-Time Signals Under Random Observation Delay

    International Nuclear Information System (INIS)

    Caballero-Aguila, R.; Jimenez-Lopez, J. D.; Hermoso-Carazo, A.; Linares-Perez, J.; Nakamori, S.

    2008-01-01

    This paper presents an approximation to the nonlinear least-squares estimation problem of discrete-time stochastic signals using nonlinear observations with additive white noise which can be randomly delayed by one sampling time. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values, zero or one, indicate that the real observation arrives on time or it is delayed and, hence, the available measurement to estimate the signal is not up-to-date. Assuming that the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are ready for use, a filtering algorithm based on linear approximations of the real observations is proposed.

  18. Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

    Science.gov (United States)

    Akimenko, Vitalii; Anguelov, Roumen

    2017-12-01

    In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

  19. Photonic single nonlinear-delay dynamical node for information processing

    Science.gov (United States)

    Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

    2012-06-01

    An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

  20. Analytical approximate solutions for a general class of nonlinear delay differential equations.

    Science.gov (United States)

    Căruntu, Bogdan; Bota, Constantin

    2014-01-01

    We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

  1. Euclidean null controllability of nonlinear infinite delay systems with ...

    African Journals Online (AJOL)

    Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...

  2. Periodicity of a class of nonlinear fuzzy systems with delays

    International Nuclear Information System (INIS)

    Yu Jiali; Yi Zhang; Zhang Lei

    2009-01-01

    The well known Takagi-Sugeno (T-S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T-S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T-S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.

  3. FREQUENCY CATASTROPHE AND CO-EXISTING ATTRACTORS IN A CELL Ca2+ NONLINEAR OSCILLATION MODEL WITH TIME DELAY*

    Institute of Scientific and Technical Information of China (English)

    应阳君; 黄祖洽

    2001-01-01

    Frequency catastrophe is found in a cell Ca2+ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.

  4. Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

    Directory of Open Access Journals (Sweden)

    S. J. Sadati

    2010-01-01

    Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.

  5. OSCILLATION OF NONLINEAR DELAY DIFFERENCE EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained.

  6. Nonlinear Cournot duopoly with implementation delays

    International Nuclear Information System (INIS)

    Matsumoto, Akio; Szidarovszky, Ferenc

    2015-01-01

    We study the effects of two delays on the local as well as on global stability of nonlinear Cournot duopoly dynamics. The two major findings are an analytical construction of the stability switching curve on which stability is lost and the numerical confirmation of the birth of aperiodic global dynamics when the stationary state is locally unstable. The delays matters and can generate various dynamics ranging from simple to complicated dynamics.

  7. Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays

    Science.gov (United States)

    Zhang, Chuan; Wang, Xingyuan; Luo, Chao; Li, Junqiu; Wang, Chunpeng

    2018-03-01

    In this paper, we focus on the robust outer synchronization problem between two nonlinear complex networks with parametric disturbances and mixed time-varying delays. Firstly, a general complex network model is proposed. Besides the nonlinear couplings, the network model in this paper can possess parametric disturbances, internal time-varying delay, discrete time-varying delay and distributed time-varying delay. Then, according to the robust control strategy, linear matrix inequality and Lyapunov stability theory, several outer synchronization protocols are strictly derived. Simple linear matrix controllers are designed to driver the response network synchronize to the drive network. Additionally, our results can be applied on the complex networks without parametric disturbances. Finally, by utilizing the delayed Lorenz chaotic system as the dynamics of all nodes, simulation examples are given to demonstrate the effectiveness of our theoretical results.

  8. Stability Analysis of Fractional-Order Nonlinear Systems with Delay

    Directory of Open Access Journals (Sweden)

    Yu Wang

    2014-01-01

    Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

  9. New Delay-Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

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    Hamid Reza Karimi

    2009-01-01

    Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.

  10. Goodwin accelerator model revisited with fixed time delays

    Science.gov (United States)

    Matsumoto, Akio; Merlone, Ugo; Szidarovszky, Ferenc

    2018-05-01

    Dynamics of Goodwin's accelerator business cycle model is reconsidered. The model is characterized by a nonlinear accelerator and an investment time delay. The role of the nonlinearity for the birth of persistent oscillations is fully discussed in the existing literature. On the other hand, not much of the role of the delay has yet been revealed. The purpose of this paper is to show that the delay really matters. In the original framework of Goodwin [6], it is first demonstrated that there is a threshold value of the delay: limit cycles arise for smaller values than the threshold and so do sawtooth oscillations for larger values. In the extended framework in which a consumption or saving delay, in addition to the investment delay, is introduced, three main results are demonstrated under assumption of the identical length of investment and consumption delays. The dynamics with consumption delay is basically the same as that of the single delay model. Second, in the case of saving delay, the steady state can coexist with the stable and unstable limit cycles in the stable case. Third, in the unstable case, there is an interval of delay in which the limit cycle or the sawtooth oscillation emerges depending on the choice of the constant initial function.

  11. Effect of state-dependent delay on a weakly damped nonlinear oscillator.

    Science.gov (United States)

    Mitchell, Jonathan L; Carr, Thomas W

    2011-04-01

    We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.

  12. Recent results on nonlinear delay control systems in honor of Miroslav Krstic

    CERN Document Server

    Pepe, Pierdomenico; Mazenc, Frederic; Karafyllis, Iasson

    2016-01-01

    This volume collects recent advances in nonlinear delay systems, with an emphasis on constructive generalized Lyapunov and predictive approaches that certify stability properties. The book is written by experts in the field and includes two chapters by Miroslav Krstic, to whom this volume is dedicated. This volume is suitable for all researchers in mathematics and engineering who deal with nonlinear delay control problems and students who would like to understand the current state of the art in the control of nonlinear delay systems.

  13. Estimation of Nonlinear Functions of State Vector for Linear Systems with Time-Delays and Uncertainties

    Directory of Open Access Journals (Sweden)

    Il Young Song

    2015-01-01

    Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.

  14. ALMOST PERIODIC SOLUTIONS TO SOME NONLINEAR DELAY DIFFERENTIAL EQUATION

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.

  15. Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays

    Science.gov (United States)

    Nguimdo, Romain Modeste

    2018-03-01

    Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.

  16. Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

    International Nuclear Information System (INIS)

    Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

    2003-01-01

    We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

  17. Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes

    International Nuclear Information System (INIS)

    Liu Tao; Zhao Jun; Hill, David J.

    2009-01-01

    In this paper, we study the global synchronization of nonlinearly coupled complex delayed dynamical networks with both directed and undirected graphs. Via Lyapunov-Krasovskii stability theory and the network topology, we investigate the global synchronization of such networks. Under the assumption that coupling coefficients are known, a family of delay-independent decentralized nonlinear feedback controllers are designed to globally synchronize the networks. When coupling coefficients are unavailable, an adaptive mechanism is introduced to synthesize a family of delay-independent decentralized adaptive controllers which guarantee the global synchronization of the uncertain networks. Two numerical examples of directed and undirected delayed dynamical network are given, respectively, using the Lorenz system as the nodes of the networks, which demonstrate the effectiveness of proposed results.

  18. Exponential synchronization of two nonlinearly non-delayed and delayed coupled complex dynamical networks

    International Nuclear Information System (INIS)

    Zheng Song

    2012-01-01

    In this paper, the exponential synchronization between two nonlinearly coupled complex networks with non-delayed and delayed coupling is investigated with Lyapunov-Krasovskii-type functionals. Based on the stability analysis of the impulsive differential equation and the linear matrix inequality, sufficient delay-dependent conditions for exponential synchronization are derived, and a linear impulsive controller and simple updated laws are also designed. Furthermore, the coupling matrices need not be symmetric or irreducible. Numerical examples are presented to verify the effectiveness and correctness of the synchronization criteria obtained.

  19. Estimation of delays and other parameters in nonlinear functional differential equations

    Science.gov (United States)

    Banks, H. T.; Lamm, P. K. D.

    1983-01-01

    A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

  20. Observer-Based Controller Design for a Class of Nonlinear Networked Control Systems with Random Time-Delays Modeled by Markov Chains

    Directory of Open Access Journals (Sweden)

    Yanfeng Wang

    2017-01-01

    Full Text Available This paper investigates the observer-based controller design problem for a class of nonlinear networked control systems with random time-delays. The nonlinearity is assumed to satisfy a global Lipschitz condition and two dependent Markov chains are employed to describe the time-delay from sensor to controller (S-C delay and the time-delay from controller to actuator (C-A delay, respectively. The transition probabilities of S-C delay and C-A delay are both assumed to be partly inaccessible. Sufficient conditions on the stochastic stability for the closed-loop systems are obtained by constructing proper Lyapunov functional. The methods of calculating the controller and the observer gain matrix are also given. Two numerical examples are used to illustrate the effectiveness of the proposed method.

  1. Dynamics of electron wave packet in a disordered chain with delayed nonlinear response

    International Nuclear Information System (INIS)

    Zhu Hongjun; Xiong Shijie

    2010-01-01

    We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron-phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schroedinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.

  2. Dynamic Output Feedback Control for Nonlinear Networked Control Systems with Random Packet Dropout and Random Delay

    Directory of Open Access Journals (Sweden)

    Shuiqing Yu

    2013-01-01

    Full Text Available This paper investigates the dynamic output feedback control for nonlinear networked control systems with both random packet dropout and random delay. Random packet dropout and random delay are modeled as two independent random variables. An observer-based dynamic output feedback controller is designed based upon the Lyapunov theory. The quantitative relationship of the dropout rate, transition probability matrix, and nonlinear level is derived by solving a set of linear matrix inequalities. Finally, an example is presented to illustrate the effectiveness of the proposed method.

  3. Chaotification of vibration isolation floating raft system via nonlinear time-delay feedback control

    International Nuclear Information System (INIS)

    Zhang Jing; Xu Daolin; Zhou Jiaxi; Li Yingli

    2012-01-01

    Highlights: ► A chaotification method based on nonlinear time-delay feedback control is present. ► An analytical function of nonlinear time-delay feedback control is derived. ► A large range of parametric domain for chaotification is obtained. ► The approach allows using small control gain. ► Design of chaotification becomes a standard process without uncertainty. - Abstract: This paper presents a chaotification method based on nonlinear time-delay feedback control for a two-dimensional vibration isolation floating raft system (VIFRS). An analytical function of nonlinear time-delay feedback control is derived. This approach can theoretically provide a systematic design of chaotification for nonlinear VIFRS and completely avoid blind and inefficient numerical search on the basis of trials and errors. Numerical simulations show that with a proper setting of control parameters the method holds the favorable aspects including the capability of chaotifying across a large range of parametric domain, the advantage of using small control and the flexibility of designing control feedback forms. The effects on chaotification performance are discussed in association with the configuration of the control parameters.

  4. A stochastic delay model for pricing debt and equity: Numerical techniques and applications

    Science.gov (United States)

    Tambue, Antoine; Kemajou Brown, Elisabeth; Mohammed, Salah

    2015-01-01

    Delayed nonlinear models for pricing corporate liabilities and European options were recently developed. Using self-financed strategy and duplication we were able to derive a Random Partial Differential Equation (RPDE) whose solutions describe the evolution of debt and equity values of a corporate in the last delay period interval in the accompanied paper (Kemajou et al., 2012) [14]. In this paper, we provide robust numerical techniques to solve the delayed nonlinear model for the corporate value, along with the corresponding RPDEs modeling the debt and equity values of the corporate. Using financial data from some firms, we forecast and compare numerical solutions from both the nonlinear delayed model and classical Merton model with the real corporate data. From this comparison, it comes up that in corporate finance the past dependence of the firm value process may be an important feature and therefore should not be ignored.

  5. Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

    Science.gov (United States)

    Polyanin, A. D.; Sorokin, V. G.

    2017-12-01

    The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

  6. Nonlinear dynamics in integrated coupled DFB lasers with ultra-short delay.

    Science.gov (United States)

    Liu, Dong; Sun, Changzheng; Xiong, Bing; Luo, Yi

    2014-03-10

    We report rich nonlinear dynamics in integrated coupled lasers with ultra-short coupling delay. Mutually stable locking, period-1 oscillation, frequency locking, quasi-periodicity and chaos are observed experimentally. The dynamic behaviors are reproduced numerically by solving coupled delay differential equations that take the variation of both frequency detuning and coupling phase into account. Moreover, it is pointed out that the round-trip frequency is not involved in the above nonlinear dynamical behaviors. Instead, the relationship between the frequency detuning Δν and the relaxation oscillation frequency νr under mutual injection are found to be critical for the various observed dynamics in mutually coupled lasers with very short delay.

  7. Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

    Directory of Open Access Journals (Sweden)

    Mingzhu Song

    2016-01-01

    Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

  8. Mixed integer nonlinear programming model of wireless pricing scheme with QoS attribute of bandwidth and end-to-end delay

    Science.gov (United States)

    Irmeilyana, Puspita, Fitri Maya; Indrawati

    2016-02-01

    The pricing for wireless networks is developed by considering linearity factors, elasticity price and price factors. Mixed Integer Nonlinear Programming of wireless pricing model is proposed as the nonlinear programming problem that can be solved optimally using LINGO 13.0. The solutions are expected to give some information about the connections between the acceptance factor and the price. Previous model worked on the model that focuses on bandwidth as the QoS attribute. The models attempt to maximize the total price for a connection based on QoS parameter. The QoS attributes used will be the bandwidth and the end to end delay that affect the traffic. The maximum goal to maximum price is achieved when the provider determine the requirement for the increment or decrement of price change due to QoS change and amount of QoS value.

  9. Relative controllability of nonlinear systems with delays in state and ...

    African Journals Online (AJOL)

    In this work, sufficient conditions are developed for the relative controllability of perturbed nonlinear systems with time varying multiple delays in control with the perturbation function having implicit derivative with delays depending on both state and control variable, using Darbo's fixed points theorem. Journal of the Nigerian ...

  10. New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

    Directory of Open Access Journals (Sweden)

    Sirada Pinjai

    2013-01-01

    Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

  11. Pinning Synchronization of Delayed Neural Networks with Nonlinear Inner-Coupling

    Directory of Open Access Journals (Sweden)

    Yangling Wang

    2011-01-01

    Full Text Available Without assuming the symmetry and irreducibility of the outer-coupling weight configuration matrices, we investigate the pinning synchronization of delayed neural networks with nonlinear inner-coupling. Some delay-dependent controlled stability criteria in terms of linear matrix inequality (LMI are obtained. An example is presented to show the application of the criteria obtained in this paper.

  12. Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method

    International Nuclear Information System (INIS)

    Souza de Paula, Aline; Savi, Marcelo Amorim

    2009-01-01

    Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge-Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.

  13. Oscillation criteria for fourth-order nonlinear delay dynamic equations

    Directory of Open Access Journals (Sweden)

    Yunsong Qi

    2013-03-01

    Full Text Available We obtain criteria for the oscillation of all solutions to a fourth-order nonlinear delay dynamic equation on a time scale that is unbounded from above. The results obtained are illustrated with examples

  14. Absolute stability of nonlinear systems with time delays and applications to neural networks

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    2001-01-01

    Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.

  15. Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

    International Nuclear Information System (INIS)

    Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.

    2005-04-01

    We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)

  16. Adaptive fuzzy observer-based stabilization of a class of uncertain time-delayed chaotic systems with actuator nonlinearities

    International Nuclear Information System (INIS)

    Shahnazi, Reza; Haghani, Adel; Jeinsch, Torsten

    2015-01-01

    An observer-based output feedback adaptive fuzzy controller is proposed to stabilize a class of uncertain chaotic systems with unknown time-varying time delays, unknown actuator nonlinearities and unknown external disturbances. The actuator nonlinearity can be backlash-like hysteresis or dead-zone. Based on universal approximation property of fuzzy systems the unknown nonlinear functions are approximated by fuzzy systems, where the consequent parts of fuzzy rules are tuned with adaptive schemes. The proposed method does not need the availability of the states and an observer based output feedback approach is proposed to estimate the states. To have more robustness and at the same time to alleviate chattering an adaptive discontinuous structure is suggested. Semi-global asymptotic stability of the overall system is ensured by proposing a suitable Lyapunov–Krasovskii functional candidate. The approach is applied to stabilize the time-delayed Lorenz chaotic system with uncertain dynamics amid significant disturbances. Analysis of simulations reveals the effectiveness of the proposed method in terms of coping well with the modeling uncertainties, nonlinearities in actuators, unknown time-varying time-delays and unknown external disturbances while maintaining asymptotic convergence

  17. On the synchronization of neural networks containing time-varying delays and sector nonlinearity

    International Nuclear Information System (INIS)

    Yan, J.-J.; Lin, J.-S.; Hung, M.-L.; Liao, T.-L.

    2007-01-01

    We present a systematic design procedure for synchronization of neural networks subject to time-varying delays and sector nonlinearity in the control input. Based on the drive-response concept and the Lyapunov stability theorem, a memoryless decentralized control law is proposed which guarantees exponential synchronization even when input nonlinearity is present. The supplementary requirement that the time-derivative of time-varying delays must be smaller than one is released for the proposed control scheme. A four-dimensional Hopfield neural network with time-varying delays is presented as the illustrative example to demonstrate the effectiveness of the proposed synchronization scheme

  18. Nonlinear Dynamic Models in Advanced Life Support

    Science.gov (United States)

    Jones, Harry

    2002-01-01

    To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

  19. A Heterogeneous Agent Model of Asspet Price with Three Time Delays

    Directory of Open Access Journals (Sweden)

    Akio Matsumoto

    2016-09-01

    Full Text Available This paper considers a continuous-time heterogeneous agent model ofa ...nancial market with one risky asset, two types of agents (i.e., thefundamentalists and the chartists, and three time delays. The chartistdemand is determined through a nonlinear function of the di¤erence be-tween the current price and a weighted moving average of the delayedprices whereas the fundamentalist demand is governed by the di¤erencebetween the current price and the fundamental value. The asset price dy-namics is described by a nonlinear delay di¤erential equation. Two mainresults are analytically and numerically shown:(i the delay destabilizes the market price and generates cyclic oscillationsaround the equilibrium;(ii under multiple delays, stability loss and gain repeatedly occurs as alength of the delay increases.

  20. Non-predictor control of a class of feedforward nonlinear systems with unknown time-varying delays

    Science.gov (United States)

    Koo, Min-Sung; Choi, Ho-Lim

    2016-08-01

    This paper generalises the several recent results on the control of feedforward time-delay nonlinear systems. First, in view of system formulation, there are unknown time-varying delays in both states and main control input. Also, the considered nonlinear system has extended feedforward nonlinearities. Second, in view of control solution, our proposed controller is a non-predictor feedback controller whereas smith-predictor type controllers are used in the several existing results. Moreover, our controller does not need any information on the unknown delays except their upper bounds. Thus, our result has certain merits in both system formulation and control solution perspective. The analysis and example are given for clear illustration.

  1. Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

    Science.gov (United States)

    Yang, Tao; Cao, Qingjie

    2018-03-01

    This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.

  2. Delay dynamical systems and applications to nonlinear machine-tool chatter

    International Nuclear Information System (INIS)

    Fofana, M.S.

    2003-01-01

    The stability behaviour of machine chatter that exhibits Hopf and degenerate bifurcations has been examined without the assumption of small delays between successive cuts. Delay dynamical system theory leading to the reduction of the infinite-dimensional character of the governing delay differential equations (DDEs) to a finite-dimensional set of ordinary differential equations have been employed. The essential mathematical arguments for these systems in the context of retarded DDEs are summarized. Then the application of these arguments in the stability study of machine-tool chatter with multiple time delays is presented. Explicit analytical expressions ensuring stable and unstable machining when perturbations are periodic, stochastic and nonlinear have been derived using the integral averaging method and Lyapunov exponents

  3. Gompertzian stochastic model with delay effect to cervical cancer growth

    International Nuclear Information System (INIS)

    Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

    2015-01-01

    In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits

  4. Gompertzian stochastic model with delay effect to cervical cancer growth

    Energy Technology Data Exchange (ETDEWEB)

    Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

    2015-02-03

    In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

  5. Intermittently chaotic oscillations for a differential-delay equation with Gaussian nonlinearity

    Science.gov (United States)

    Hamilton, Ian

    1992-01-01

    For a differential-delay equation the time dependence of the variable is a function of the variable at a previous time. We consider a differential-delay equation with Gaussian nonlinearity that displays intermittent chaos. Although not the first example of a differential-delay equation that displays such behavior, for this example the intermittency is classified as type III, and the origin of the intermittent chaos may be qualitatively understood from the limiting forms of the equation for large and small variable magnitudes.

  6. Stability analysis for a delay differential equations model of a hydraulic turbine speed governor

    Science.gov (United States)

    Halanay, Andrei; Safta, Carmen A.; Dragoi, Constantin; Piraianu, Vlad F.

    2017-01-01

    The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is introduced as a time delay. The delays can characterize different running conditions of the speed governor. For example, it is considered that spool displacement of hydraulic amplifier might be blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay in comparison to the time control. Numerical simulations are presented in a comparative manner. A stability analysis of the hydraulic control system is performed, too. Conclusions of the dynamic behavior using the DDE model of a hydraulic turbine speed governor are useful in modeling and controlling hydropower plants.

  7. A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes

    Directory of Open Access Journals (Sweden)

    Qi-Zhi Zhang

    2005-01-01

    Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.

  8. On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Fang Li

    2012-01-01

    Full Text Available Of concern is a class of nonlinear neutral fractional integrodifferential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. An example is given to illustrate the existence result.

  9. A ternary logic model for recurrent neuromime networks with delay.

    Science.gov (United States)

    Hangartner, R D; Cull, P

    1995-07-01

    In contrast to popular recurrent artificial neural network (RANN) models, biological neural networks have unsymmetric structures and incorporate significant delays as a result of axonal propagation. Consequently, biologically inspired neural network models are more accurately described by nonlinear differential-delay equations rather than nonlinear ordinary differential equations (ODEs), and the standard techniques for studying the dynamics of RANNs are wholly inadequate for these models. This paper develops a ternary-logic based method for analyzing these networks. Key to the technique is the realization that a nonzero delay produces a bounded stability region. This result significantly simplifies the construction of sufficient conditions for characterizing the network equilibria. If the network gain is large enough, each equilibrium can be classified as either asymptotically stable or unstable. To illustrate the analysis technique, the swim central pattern generator (CPG) of the sea slug Tritonia diomedea is examined. For wide range of reasonable parameter values, the ternary analysis shows that none of the network equilibria are stable, and thus the network must oscillate. The results show that complex synaptic dynamics are not necessary for pattern generation.

  10. Global stability for infectious disease models that include immigration of infected individuals and delay in the incidence

    Directory of Open Access Journals (Sweden)

    Chelsea Uggenti

    2018-03-01

    Full Text Available We begin with a detailed study of a delayed SI model of disease transmission with immigration into both classes. The incidence function allows for a nonlinear dependence on the infected population, including mass action and saturating incidence as special cases. Due to the immigration of infectives, there is no disease-free equilibrium and hence no basic reproduction number. We show there is a unique endemic equilibrium and that this equilibrium is globally asymptotically stable for all parameter values. The results include vector-style delay and latency-style delay. Next, we show that previous global stability results for an SEI model and an SVI model that include immigration of infectives and non-linear incidence but not delay can be extended to systems with vector-style delay and latency-style delay.

  11. Delay-Dependent Finite-Time H∞ Controller Design for a Kind of Nonlinear Descriptor Systems via a T-S Fuzzy Model

    Directory of Open Access Journals (Sweden)

    Baoyan Zhu

    2015-01-01

    Full Text Available Delay-dependent finite-time H∞ controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time H∞ controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the H∞ performance to a prescribed disturbance attenuation level γ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI. Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a H∞ performance level.

  12. The role of delay in the dynamics of nuclear reactors

    International Nuclear Information System (INIS)

    Svitra, D.; Bucys, K.

    1999-01-01

    The stability of nuclear reactors based on nonlinear models of reactor dynamics including the action of delayed neutrons is analysed. The point model of reactor dynamics with the system of seven nonlinear simple differential equations was changed to the system of two nonlinear differential equations including the action of delay. The method of the theory of bifurcations for nonlinear differential equations with delay is used. (author)

  13. Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

    OpenAIRE

    Luo, Hongwei; Zhang, Jiangang; Du, Wenju; Lu, Jiarong; An, Xinlei

    2017-01-01

    A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the dire...

  14. Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

    2013-01-01

    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

  15. Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay

    Directory of Open Access Journals (Sweden)

    Azizollah Babakhani

    2010-01-01

    Full Text Available We investigate the existence and uniqueness of positive solution for system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.

  16. Oscillation of solutions to neutral nonlinear impulsive hyperbolic equations with several delays

    Directory of Open Access Journals (Sweden)

    Jichen Yang

    2013-01-01

    Full Text Available In this article, we study oscillatory properties of solutions to neutral nonlinear impulsive hyperbolic partial differential equations with several delays. We establish sufficient conditions for oscillation of all solutions.

  17. Local Stability of AIDS Epidemic Model Through Treatment and Vertical Transmission with Time Delay

    Science.gov (United States)

    Novi W, Cascarilla; Lestari, Dwi

    2016-02-01

    This study aims to explain stability of the spread of AIDS through treatment and vertical transmission model. Human with HIV need a time to positively suffer AIDS. The existence of a time, human with HIV until positively suffer AIDS can be delayed for a time so that the model acquired is the model with time delay. The model form is a nonlinear differential equation with time delay, SIPTA (susceptible-infected-pre AIDS-treatment-AIDS). Based on SIPTA model analysis results the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point with and without time delay are local asymptotically stable if the basic reproduction number is less than one. The endemic equilibrium point will be local asymptotically stable if the time delay is less than the critical value of delay, unstable if the time delay is more than the critical value of delay, and bifurcation occurs if the time delay is equal to the critical value of delay.

  18. Stability Control of Force-Reflected Nonlinear Multilateral Teleoperation System under Time-Varying Delays

    Directory of Open Access Journals (Sweden)

    Da Sun

    2016-01-01

    Full Text Available A novel control algorithm based on the modified wave-variable controllers is proposed to achieve accurate position synchronization and reasonable force tracking of the nonlinear single-master-multiple-slave teleoperation system and simultaneously guarantee overall system’s stability in the presence of large time-varying delays. The system stability in different scenarios of human and environment situations has been analyzed. The proposed method is validated through experimental work based on the 3-DOF trilateral teleoperation system consisting of three different manipulators. The experimental results clearly demonstrate the feasibility of the proposed algorithm to achieve high transparency and robust stability in nonlinear single-master-multiple-slave teleoperation system in the presence of time-varying delays.

  19. Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities

    International Nuclear Information System (INIS)

    Chen, S.-F.

    2009-01-01

    The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.

  20. Oscillation criteria for third order nonlinear delay differential equations with damping

    Directory of Open Access Journals (Sweden)

    Said R. Grace

    2015-01-01

    Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.

  1. Stability of a general delayed virus dynamics model with humoral immunity and cellular infection

    Science.gov (United States)

    Elaiw, A. M.; Raezah, A. A.; Alofi, A. S.

    2017-06-01

    In this paper, we investigate the dynamical behavior of a general nonlinear model for virus dynamics with virus-target and infected-target incidences. The model incorporates humoral immune response and distributed time delays. The model is a four dimensional system of delay differential equations where the production and removal rates of the virus and cells are given by general nonlinear functions. We derive the basic reproduction parameter R˜0 G and the humoral immune response activation number R˜1 G and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations.

  2. Multiple bifurcations and periodic 'bubbling' in a delay population model

    International Nuclear Information System (INIS)

    Peng Mingshu

    2005-01-01

    In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc

  3. New Results on Robust Model Predictive Control for Time-Delay Systems with Input Constraints

    Directory of Open Access Journals (Sweden)

    Qing Lu

    2014-01-01

    Full Text Available This paper investigates the problem of model predictive control for a class of nonlinear systems subject to state delays and input constraints. The time-varying delay is considered with both upper and lower bounds. A new model is proposed to approximate the delay. And the uncertainty is polytopic type. For the state-feedback MPC design objective, we formulate an optimization problem. Under model transformation, a new model predictive controller is designed such that the robust asymptotical stability of the closed-loop system can be guaranteed. Finally, the applicability of the presented results are demonstrated by a practical example.

  4. Effects of delayed nonlinear response on wave packet dynamics in one-dimensional generalized Fibonacci chains

    International Nuclear Information System (INIS)

    Zhang, Jianxin; Zhang, Zhenjun; Tong, Peiqing

    2013-01-01

    We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth

  5. Effects of delayed nonlinear response on wave packet dynamics in one-dimensional generalized Fibonacci chains

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Jianxin; Zhang, Zhenjun [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Tong, Peiqing, E-mail: pqtong@njnu.edu.cn [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023 (China)

    2013-07-15

    We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth.

  6. Neimark-Sacker bifurcation for the discrete-delay Kaldor model

    International Nuclear Information System (INIS)

    Dobrescu, Loretti I.; Opris, Dumitru

    2009-01-01

    We consider a discrete-delay time, Kaldor nonlinear business cycle model in income and capital. Given an investment function, resembling the one discussed by Rodano, we use the linear approximation analysis to state the local stability property and local bifurcations, in the parameter space. Finally, we will give some numerical examples to justify the theoretical results.

  7. Rotating and standing waves in a diffractive nonlinear optical system with delayed feedback under O(2) Hopf bifurcation

    Science.gov (United States)

    Budzinskiy, S. S.; Razgulin, A. V.

    2017-08-01

    In this paper we study one-dimensional rotating and standing waves in a model of an O(2)-symmetric nonlinear optical system with diffraction and delay in the feedback loop whose dynamics is governed by a system of coupled delayed parabolic equation and linear Schrodinger-type equation. We elaborate a two-step approach: transition to a rotating coordinate system to obtain the profiles of the waves as small parameter expansions and the normal form technique to study their qualitative dynamic behavior and stability. Theoretical results stand in a good agreement with direct computer simulations presented.

  8. EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.

  9. Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.

  10. Recurrent-Neural-Network-Based Multivariable Adaptive Control for a Class of Nonlinear Dynamic Systems With Time-Varying Delay.

    Science.gov (United States)

    Hwang, Chih-Lyang; Jan, Chau

    2016-02-01

    At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.

  11. Periodic solutions of certain third order nonlinear differential systems with delay

    International Nuclear Information System (INIS)

    Tejumola, H.O.; Afuwape, A.U.

    1990-12-01

    This paper investigates the existence of 2π-periodic solutions of systems of third-order nonlinear differential equations, with delay, under varied assumptions. The results obtained extend earlier works of Tejumola and generalize to third order systems those of Conti, Iannacci and Nkashama as well as DePascale and Iannacci and Iannacci and Nkashama. 16 refs

  12. Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information

    Science.gov (United States)

    Li, Songting; Xiao, Yanyang; Zhou, Douglas; Cai, David

    2018-05-01

    The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

  13. Inverse Problems for Nonlinear Delay Systems

    Science.gov (United States)

    2011-03-15

    population dynamics. We consider the delay between birth and adulthood for neonate pea aphids and present a mathematical model that treats this delay as...which there is currently no known cure. For HIV, the core of the virus is composed of single-stranded viral RNA and protein components. As depicted in...at a CD4 receptor site and the viral core is injected into the cell. Once inside, the protein components enable transcription and integration of the

  14. Analysis of backward differentiation formula for nonlinear differential-algebraic equations with 2 delays.

    Science.gov (United States)

    Sun, Leping

    2016-01-01

    This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.

  15. H∞ Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory

    Directory of Open Access Journals (Sweden)

    Weiwei Sun

    2015-01-01

    Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

  16. Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity

    Directory of Open Access Journals (Sweden)

    Leonid Berezansky

    2005-04-01

    Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.

  17. Estimation of time delay and wavelength shift for highly nonlinear multilayer waveguide by using time transformation approach

    Science.gov (United States)

    Chatterjee, Roshmi; Basu, Mousumi

    2018-02-01

    The well known time transformation method is used here to derive the temporal and spectral electric field distribution at the output end of a multilayer waveguide which consists of different layers of Kerr nonlinear media. A highly nonlinear CS 3-68 glass is considered as one of the materials of the waveguide which mainly comprises of different chalcogenide glass layers. The results indicate that there is sufficient time delay as well as frequency shift between the input and output pulses which is associated with the phenomenon of adiabatic wavelength conversion (AWC). Depending on different arrangements of materials, the time delay and frequency shift can be changed. As a result an input pulse in visible green region can be blue-shifted or red-shifted according to the choices of refractive index of the non-dispersive Kerr nonlinear media. The results show that under certain conditions the input pulse is broadened or compressed for different combinations of materials. This process of AWC also includes the variation of temporal and spectral phase, time delay, temporal peak power etc. For different input pulse shapes the change in time delay is also presented. The study may be useful to find applications of AWC in optical resonators or optical signal processing to be applicable to different photonic devices.

  18. Nonlinear Delay Discrete Inequalities and Their Applications to Volterra Type Difference Equations

    Directory of Open Access Journals (Sweden)

    Yu Wu

    2010-01-01

    Full Text Available Delay discrete inequalities with more than one nonlinear term are discussed, which generalize some known results and can be used in the analysis of various problems in the theory of certain classes of discrete equations. Application examples to show boundedness and uniqueness of solutions of a Volterra type difference equation are also given.

  19. Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation

    International Nuclear Information System (INIS)

    Ji, J.C.; Hansen, Colin H.

    2005-01-01

    The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions

  20. Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

    Directory of Open Access Journals (Sweden)

    Chengrong Xie

    2013-01-01

    Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

  1. A semi-analytical approach for solving of nonlinear systems of functional differential equations with delay

    Science.gov (United States)

    Rebenda, Josef; Šmarda, Zdeněk

    2017-07-01

    In the paper, we propose a correct and efficient semi-analytical approach to solve initial value problem for systems of functional differential equations with delay. The idea is to combine the method of steps and differential transformation method (DTM). In the latter, formulas for proportional arguments and nonlinear terms are used. An example of using this technique for a system with constant and proportional delays is presented.

  2. Effects of linear and nonlinear time-delayed feedback on the noise-enhanced stability phenomenon in a periodically driven bistable system

    International Nuclear Information System (INIS)

    Jia, Zheng-Lin; Mei, Dong-Cheng

    2011-01-01

    We investigate numerically the effects of time delay on the phenomenon of noise-enhanced stability (NES) in a periodically modulated bistable system. Three types of time-delayed feedback, including linear delayed feedback, nonlinear delayed feedback and global delayed feedback, are considered. We find a non-monotonic behaviour of the mean first-passage time (MFPT) as a function of the delay time τ, with a maximum in the case of linear delayed feedback and with a minimum in the case of nonlinear delayed feedback. There are two peculiar values of τ around which the NES phenomenon is enhanced or weakened. For the case of global delayed feedback, the increase of τ always weakens the NES phenomenon. Moreover, we also show that the amplitude A and the frequency Ω of the periodic forcing play an opposite role in the NES phenomenon, i.e. the increase of A weakens the NES effect while the increase of Ω enhances it. These observations demonstrate that the time-delayed feedback can be used as a feasible control scheme for the NES phenomenon

  3. Prediction-Based Control for Nonlinear Systems with Input Delay

    Directory of Open Access Journals (Sweden)

    I. Estrada-Sánchez

    2017-01-01

    Full Text Available This work has two primary objectives. First, it presents a state prediction strategy for a class of nonlinear Lipschitz systems subject to constant time delay in the input signal. As a result of a suitable change of variable, the state predictor asymptotically provides the value of the state τ units of time ahead. Second, it proposes a solution to the stabilization and trajectory tracking problems for the considered class of systems using predicted states. The predictor-controller convergence is proved by considering a complete Lyapunov functional. The proposed predictor-based controller strategy is evaluated using numerical simulations.

  4. Stability and bifurcation analysis in a delayed SIR model

    International Nuclear Information System (INIS)

    Jiang Zhichao; Wei Junjie

    2008-01-01

    In this paper, a time-delayed SIR model with a nonlinear incidence rate is considered. The existence of Hopf bifurcations at the endemic equilibrium is established by analyzing the distribution of the characteristic values. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out

  5. Analysis of deterministic cyclic gene regulatory network models with delays

    CERN Document Server

    Ahsen, Mehmet Eren; Niculescu, Silviu-Iulian

    2015-01-01

    This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.

  6. A penalized framework for distributed lag non-linear models.

    Science.gov (United States)

    Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G

    2017-09-01

    Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

  7. Adaptive Neural Control for a Class of Outputs Time-Delay Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Ruliang Wang

    2012-01-01

    Full Text Available This paper considers an adaptive neural control for a class of outputs time-delay nonlinear systems with perturbed or no. Based on RBF neural networks, the radius basis function (RBF neural networks is employed to estimate the unknown continuous functions. The proposed control guarantees that all closed-loop signals remain bounded. The simulation results demonstrate the effectiveness of the proposed control scheme.

  8. Neimark-Sacker bifurcation for the discrete-delay Kaldor-Kalecki model

    International Nuclear Information System (INIS)

    Dobrescu, Loretti I.; Opris, Dumitru

    2009-01-01

    The present work will focus on a Kaldor-Kalecki nonlinear business cycle model in income and capital, with discrete time and delay argument characteristics. What it will state, considering an investment function similar to the one proposed by Rodano and using the linear approximation analysis, are the local stability property and local bifurcations conditions, given the parameter space. Numerical examples will be given in the end, to support the theoretical results obtained.

  9. Fuzzy model-based adaptive synchronization of time-delayed chaotic systems

    International Nuclear Information System (INIS)

    Vasegh, Nastaran; Majd, Vahid Johari

    2009-01-01

    In this paper, fuzzy model-based synchronization of a class of first order chaotic systems described by delayed-differential equations is addressed. To design the fuzzy controller, the chaotic system is modeled by Takagi-Sugeno fuzzy system considering the properties of the nonlinear part of the system. Assuming that the parameters of the chaotic system are unknown, an adaptive law is derived to estimate these unknown parameters, and the stability of error dynamics is guaranteed by Lyapunov theory. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.

  10. Electrocardiogram classification using delay differential equations.

    Science.gov (United States)

    Lainscsek, Claudia; Sejnowski, Terrence J

    2013-06-01

    Time series analysis with nonlinear delay differential equations (DDEs) reveals nonlinear as well as spectral properties of the underlying dynamical system. Here, global DDE models were used to analyze 5 min data segments of electrocardiographic (ECG) recordings in order to capture distinguishing features for different heart conditions such as normal heart beat, congestive heart failure, and atrial fibrillation. The number of terms and delays in the model as well as the order of nonlinearity of the model have to be selected that are the most discriminative. The DDE model form that best separates the three classes of data was chosen by exhaustive search up to third order polynomials. Such an approach can provide deep insight into the nature of the data since linear terms of a DDE correspond to the main time-scales in the signal and the nonlinear terms in the DDE are related to nonlinear couplings between the harmonic signal parts. The DDEs were able to detect atrial fibrillation with an accuracy of 72%, congestive heart failure with an accuracy of 88%, and normal heart beat with an accuracy of 97% from 5 min of ECG, a much shorter time interval than required to achieve comparable performance with other methods.

  11. Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

    KAUST Repository

    Abdelkefi, Abdessattar

    2013-06-18

    In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.

  12. Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

    Science.gov (United States)

    Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo

    2014-07-01

    Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs. Copyright © 2014 Elsevier Ltd. All rights reserved.

  13. Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .

  14. The influences of delay time on the stability of a market model with stochastic volatility

    Science.gov (United States)

    Li, Jiang-Cheng; Mei, Dong-Cheng

    2013-02-01

    The effects of the delay time on the stability of a market model are investigated, by using a modified Heston model with a cubic nonlinearity and cross-correlated noise sources. These results indicate that: (i) There is an optimal delay time τo which maximally enhances the stability of the stock price under strong demand elasticity of stock price, and maximally reduces the stability of the stock price under weak demand elasticity of stock price; (ii) The cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time τo. Moreover, the probability density function of the escape time of stock price returns, the probability density function of the returns and the correlation function of the returns are compared with other literatures.

  15. Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

    Science.gov (United States)

    Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

    2015-12-01

    This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

  16. Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

    Directory of Open Access Journals (Sweden)

    Hongwei Luo

    2017-01-01

    Full Text Available A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

  17. Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

    Directory of Open Access Journals (Sweden)

    Pablo César Rodríguez Gómez

    2017-05-01

    Full Text Available Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis. Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior. Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed. Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system. Language: English

  18. Synchronization of delay-coupled nonlinear oscillators : an approach based on the stability analysis of synchronized equilibria

    NARCIS (Netherlands)

    Michiels, W.; Nijmeijer, H.

    2009-01-01

    We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the

  19. LDRD report nonlinear model reduction

    Energy Technology Data Exchange (ETDEWEB)

    Segalman, D.; Heinstein, M.

    1997-09-01

    The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.

  20. A new lattice hydrodynamic model based on control method considering the flux change rate and delay feedback signal

    Science.gov (United States)

    Qin, Shunda; Ge, Hongxia; Cheng, Rongjun

    2018-02-01

    In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.

  1. Dynamical Behaviors in Complex-Valued Love Model With or Without Time Delays

    Science.gov (United States)

    Deng, Wei; Liao, Xiaofeng; Dong, Tao

    2017-12-01

    In this paper, a novel version of nonlinear model, i.e. a complex-valued love model with two time delays between two individuals in a love affair, has been proposed. A notable feature in this model is that we separate the emotion of one individual into real and imaginary parts to represent the variation and complexity of psychophysiological emotion in romantic relationship instead of just real domain, and make our model much closer to reality. This is because love is a complicated cognitive and social phenomenon, full of complexity, diversity and unpredictability, which refers to the coexistence of different aspects of feelings, states and attitudes ranging from joy and trust to sadness and disgust. By analyzing associated characteristic equation of linearized equations for our model, it is found that the Hopf bifurcation occurs when the sum of time delays passes through a sequence of critical value. Stability of bifurcating cyclic love dynamics is also derived by applying the normal form theory and the center manifold theorem. In addition, it is also shown that, for some appropriate chosen parameters, chaotic behaviors can appear even without time delay.

  2. Fuzzy delay model based fault simulator for crosstalk delay fault test ...

    Indian Academy of Sciences (India)

    In this paper, a fuzzy delay model based crosstalk delay fault simulator is proposed. As design trends move towards nanometer technologies, more number of new parameters affects the delay of the component. Fuzzy delay models are ideal for modelling the uncertainty found in the design and manufacturing steps.

  3. Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach

    Directory of Open Access Journals (Sweden)

    Jing Lei

    2013-01-01

    Full Text Available The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.

  4. Modelling delays in pharmacokinetics

    International Nuclear Information System (INIS)

    Farooqi, Z.H.; Lambrecht, R.M.

    1990-01-01

    Linear system analysis has come to form the backbone of pharmacokinetics. Natural systems usually involve time delays, thus models incorporating them would be an order closer approximation to the real world compared to those that do not. Delays may be modelled in several ways. The approach considered in this study is to have a discrete-time delay dependent rate with the delay respresenting the duration between the entry of a drug into a compartment and its release in some form (may be as a metabolite) from the compartment. Such a delay may be because of one or more of several physiological reasons, like, formation of a reservoir, slow metabolism, or receptor binding. The mathematical structure this gives rise to is a system of delay-differential equations. Examples are given of simple one and two compartment systems with drugs like bumetanide, carbamazepine, and quinolone-caffeine interaction. In these examples generally a good fit is obtained and the suggested models form a good approximation. 21 refs., 6 figs

  5. Distributed nonlinear optical response

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov

    2005-01-01

    of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

  6. Nonlinear delay monopoly with bounded rationality

    International Nuclear Information System (INIS)

    Matsumoto, Akio; Szidarovszky, Ferenc

    2012-01-01

    The purpose of this paper is to study the dynamics of a monopolistic firm in a continuous-time framework. The firm is assumed to be boundedly rational and to experience time delays in obtaining and implementing information on output. The dynamic adjustment process is based on the gradient of the expected profit. The paper is divided into three parts: we examine delay effects on dynamics caused by one-time delay and two-time delays in the first two parts. Global dynamics and analytical results on local dynamics are numerically confirmed in the third part. Four main results are demonstrated. First, the stability switch from stability to instability occurs only once in the case of a single delay. Second, the alternation of stability and instability can continue if two time delays are involved. Third, the occurence of Hopf bifurcation is analytically shown if stability is lost. Finally, in a bifurcation process, there are a period-doubling cascade to chaos and a period-halving cascade to the equilibrium point in the case of two time delays if the difference between the two delays is large.

  7. Generalized Nonlinear Yule Models

    OpenAIRE

    Lansky, Petr; Polito, Federico; Sacerdote, Laura

    2016-01-01

    With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth...

  8. Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

    Directory of Open Access Journals (Sweden)

    Chen Yuming

    2011-01-01

    Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

  9. Modeling nonlinearities in MEMS oscillators.

    Science.gov (United States)

    Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

    2013-08-01

    We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

  10. Prediction of partial synchronization in delay-coupled nonlinear oscillators, with application to Hindmarsh–Rose neurons

    International Nuclear Information System (INIS)

    Ünal, Hakkı Ulaş; Michiels, Wim

    2013-01-01

    The full synchronization of coupled nonlinear oscillators has been widely studied. In this paper we investigate conditions for which partial synchronization of time-delayed diffusively coupled systems arises. The coupling configuration of the systems is described by a directed graph. As a novel quantitative result we first give necessary and sufficient conditions for the presence of forward invariant sets characterized by partially synchronous motion. These conditions can easily be checked from the eigenvalues and eigenvectors of the graph Laplacian. Second, we perform stability analysis of the synchronized equilibria in a (gain,delay) parameter space. For this analysis the coupled nonlinear systems are linearized around the synchronized equilibria and then the resulting characteristic function is factorized. By such a factorization, it is shown that the relation between the behaviour of different agents at the zero of the characteristic function depends on the structure of the eigenvectors of the weighted Laplacian matrix. By determining the structure of the solutions in the unstable manifold, combined with the characterization of invariant sets, we predict which partially synchronous regimes occur and estimate the corresponding coupling gain and delay values. We apply the obtained results to networks of coupled Hindmarsh–Rose neurons and verify the occurrence of the expected partially synchronous regimes by using a numerical simulation. We also make a comparison with an existing approach based on Lyapunov functionals. (paper)

  11. Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

    Science.gov (United States)

    Meng, Xin-You; Wu, Yu-Qian

    In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

  12. ORIGINAL ARTICLE Stability Analysis of Delayed Cournot Model in ...

    African Journals Online (AJOL)

    HP

    and Lyapunov method of nonlinear stability analysis are employed. It is ascertained ... and the rival player makes decision without delay, it leads to instability of the dynamic system at ... phenomena such as economic growth, prediction and ...

  13. Chaos control in delayed chaotic systems via sliding mode based delayed feedback

    Energy Technology Data Exchange (ETDEWEB)

    Vasegh, Nastaran [Faculty of Electrical Engineering, K.N. Toosi University of Technology, Seyed Khandan Bridge, Shariati St. 16314, P.O. Box 16315-1355, Tehran (Iran, Islamic Republic of)], E-mail: vasegh@eetd.kntu.ac.ir; Sedigh, Ali Khaki [Faculty of Electrical Engineering, K.N. Toosi University of Technology, Seyed Khandan Bridge, Shariati St. 16314, P.O. Box 16315-1355, Tehran (Iran, Islamic Republic of)

    2009-04-15

    This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey-Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

  14. Chaos control in delayed chaotic systems via sliding mode based delayed feedback

    International Nuclear Information System (INIS)

    Vasegh, Nastaran; Sedigh, Ali Khaki

    2009-01-01

    This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey-Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

  15. Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

    Science.gov (United States)

    Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

    2007-10-01

    Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

  16. Memorized discrete systems and time-delay

    CERN Document Server

    Luo, Albert C J

    2017-01-01

    This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

  17. A Novel Scheme for Optimal Control of a Nonlinear Delay Differential Equations Model to Determine Effective and Optimal Administrating Chemotherapy Agents in Breast Cancer.

    Science.gov (United States)

    Ramezanpour, H R; Setayeshi, S; Akbari, M E

    2011-01-01

    Determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. The most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. This is because in these cases, the therapy not only kills the tumor cells, but also kills some of the healthy tissues and causes serious damages. In this paper we investigate optimal drug scheduling effect for breast cancer model which consist of nonlinear ordinary differential time-delay equations. In this paper, a mathematical model of breast cancer tumors is discussed and then optimal control theory is applied to find out the optimal drug adjustment as an input control of system. Finally we use Sensitivity Approach (SA) to solve the optimal control problem. The goal of this paper is to determine optimal and effective scheme for administering the chemotherapy agent, so that the tumor is eradicated, while the immune systems remains above a suitable level. Simulation results confirm the effectiveness of our proposed procedure. In this paper a new scheme is proposed to design a therapy protocol for chemotherapy in Breast Cancer. In contrast to traditional pulse drug delivery, a continuous process is offered and optimized, according to the optimal control theory for time-delay systems.

  18. On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

    Directory of Open Access Journals (Sweden)

    Youliang Fu

    2016-01-01

    Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

  19. Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

    KAUST Repository

    Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.; Zidan, Mohammed A.

    2012-01-01

    This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

  20. Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

    KAUST Repository

    Mansingka, Abhinav S.

    2012-07-29

    This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

  1. Exponential L2-L∞ Filtering for a Class of Stochastic System with Mixed Delays and Nonlinear Perturbations

    Directory of Open Access Journals (Sweden)

    Zhaohui Chen

    2013-01-01

    Full Text Available The delay-dependent exponential L2-L∞ performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the L2-L∞ filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs. By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed L2-L∞ performance γ. Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.

  2. Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

    Directory of Open Access Journals (Sweden)

    Fei Chen

    2013-01-01

    Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

  3. Nonlinear Modeling by Assembling Piecewise Linear Models

    Science.gov (United States)

    Yao, Weigang; Liou, Meng-Sing

    2013-01-01

    To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

  4. Relaxation Cycles in a Generalized Neuron Model with Two Delays

    Directory of Open Access Journals (Sweden)

    S. D. Glyzin

    2013-01-01

    Full Text Available A method of modeling the phenomenon of bursting behavior in neural systems based on delay equations is proposed. A singularly perturbed scalar nonlinear differentialdifference equation of Volterra type is a mathematical model of a neuron and a separate pulse containing one function without delay and two functions with different lags. It is established that this equation, for a suitable choice of parameters, has a stable periodic motion with any preassigned number of bursts in the time interval of the period length. To prove this assertion we first go to a relay-type equation and then determine the asymptotic solutions of a singularly perturbed equation. On the basis of this asymptotics the Poincare operator is constructed. The resulting operator carries a closed bounded convex set of initial conditions into itself, which suggests that it has at least one fixed point. The Frechet derivative evaluation of the succession operator, made in the paper, allows us to prove the uniqueness and stability of the resulting relax of the periodic solution.

  5. Synchronization of delay-coupled nonlinear oscillators: an approach based on the stability analysis of synchronized equilibria.

    Science.gov (United States)

    Michiels, Wim; Nijmeijer, Henk

    2009-09-01

    We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties

  6. Adaptive regression for modeling nonlinear relationships

    CERN Document Server

    Knafl, George J

    2016-01-01

    This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the s...

  7. Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

    International Nuclear Information System (INIS)

    Cui Baotong; Lou Xuyang

    2009-01-01

    In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme

  8. Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise.

    Science.gov (United States)

    Chen, Po-Wei; Chen, Bor-Sen

    2011-08-01

    Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods. Copyright © 2011 Elsevier Inc. All rights reserved.

  9. Robust Stability for Nonlinear Systems with Time-Varying Delay and Uncertainties via the H∞ Quasi-Sliding Mode Control

    Directory of Open Access Journals (Sweden)

    Yi-You Hou

    2014-01-01

    Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.

  10. Global exponential stability of BAM neural networks with transmission delays and nonlinear impulses

    International Nuclear Information System (INIS)

    Huang Zhenkun; Xia Yonghui

    2008-01-01

    In this paper, a class of bidirectional associative memory (BAM) networks with transmission delays and nonlinear impulses are studied. Some new sufficient conditions are established for the existence and global exponential stability of a unique equilibrium, which generalize and improve the previously known results. The sufficient conditions are easy to verify and when the impulsive jumps are linear or absent the results reduce to those of common impulsive or non-impulsive systems. Finally, an example is given to show the feasibility and effectiveness of our results

  11. Bifurcation and chaotic behavior in the Euler method for a Kaplan-Yorke prototype delay model

    International Nuclear Information System (INIS)

    Peng Mingshu

    2004-01-01

    A discrete model with a simple cubic nonlinearity term is treated in the study the rich dynamics of a prototype delayed dynamical system under Euler discretization. The effect of breaking the symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include multiple steady states, complex periodic oscillations, chaos by period doubling bifurcations

  12. Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

    Energy Technology Data Exchange (ETDEWEB)

    Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)

    2014-09-25

    Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.

  13. Nonlinear modelling of polymer electrolyte membrane fuel cell stack using nonlinear cancellation technique

    International Nuclear Information System (INIS)

    Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar

    2014-01-01

    Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range

  14. Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

    Directory of Open Access Journals (Sweden)

    Hongtao Yang

    2018-01-01

    Full Text Available This paper proposes a novel strong tracking filter (STF, which is suitable for dealing with the filtering problem of nonlinear systems when the following cases occur: that is, the constructed model does not match the actual system, the measurements have the one-step random delay, and the process and measurement noises are correlated at the same epoch. Firstly, a framework of decoupling filter (DF based on equivalent model transformation is derived. Further, according to the framework of DF, a new extended Kalman filtering (EKF algorithm via using first-order linearization approximation is developed. Secondly, the computational process of the suboptimal fading factor is derived on the basis of the extended orthogonality principle (EOP. Thirdly, the ultimate form of the proposed STF is obtained by introducing the suboptimal fading factor into the above EKF algorithm. The proposed STF can automatically tune the suboptimal fading factor on the basis of the residuals between available and predicted measurements and further the gain matrices of the proposed STF tune online to improve the filtering performance. Finally, the effectiveness of the proposed STF has been proved through numerical simulation experiments.

  15. Bifurcation analysis and spatio-temporal patterns of nonlinear oscillations in a delayed neural network with unidirectional coupling

    International Nuclear Information System (INIS)

    Song Yongli; Tadé, Moses O; Zhang Tonghua

    2009-01-01

    In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained

  16. Stochastic Stability for Time-Delay Markovian Jump Systems with Sector-Bounded Nonlinearities and More General Transition Probabilities

    Directory of Open Access Journals (Sweden)

    Dan Ye

    2013-01-01

    Full Text Available This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

  17. Time-delayed feedback control of diffusion in random walkers

    Science.gov (United States)

    Ando, Hiroyasu; Takehara, Kohta; Kobayashi, Miki U.

    2017-07-01

    Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.

  18. Delay-Dependent Control for Networked Control Systems with Large Delays

    Directory of Open Access Journals (Sweden)

    Yilin Wang

    2013-01-01

    Full Text Available We consider the problems of robust stability and control for a class of networked control systems with long-time delays. Firstly, a nonlinear discrete time model with mode-dependent time delays is proposed by converting the uncertainty of time delay into the uncertainty of parameter matrices. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of linear matrix inequalities (LMIs. Then, we extend the results to a more practical case where the subsystem occurrence probabilities are uncertain. Finally, a simulation example is presented to show the efficacy of the proposed method.

  19. Analysis of degree of nonlinearity and stochastic nature of HRV signal during meditation using delay vector variance method.

    Science.gov (United States)

    Reddy, L Ram Gopal; Kuntamalla, Srinivas

    2011-01-01

    Heart rate variability analysis is fast gaining acceptance as a potential non-invasive means of autonomic nervous system assessment in research as well as clinical domains. In this study, a new nonlinear analysis method is used to detect the degree of nonlinearity and stochastic nature of heart rate variability signals during two forms of meditation (Chi and Kundalini). The data obtained from an online and widely used public database (i.e., MIT/BIH physionet database), is used in this study. The method used is the delay vector variance (DVV) method, which is a unified method for detecting the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. From the results it is clear that there is a significant change in the nonlinearity and stochastic nature of the signal before and during the meditation (p value > 0.01). During Chi meditation there is a increase in stochastic nature and decrease in nonlinear nature of the signal. There is a significant decrease in the degree of nonlinearity and stochastic nature during Kundalini meditation.

  20. Nonlinear dynamics of regenerative cutting processes-Comparison of two models

    International Nuclear Information System (INIS)

    Wang, X.S.; Hu, J.; Gao, J.B.

    2006-01-01

    Understanding the nonlinear dynamics of cutting processes is essential for the improvement of machining technology. We study machine cutting processes by two different models, one has been recently introduced by Litak [Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons and Fractals 2002;13:1531-5] and the other is the classic delay differential equation model. Although chaotic solutions have been found in both models, well known routes to chaos, such as period-doubling or quasi-periodic motion to chaos are not observed in either model. Careful analysis shows that the chaotic motion from the Litak's model has sharper spectral peaks, a smaller correlation dimension and a smaller value for the largest positive Lyapunov exponent. Implications to the control of chaos in cutting processes are discussed

  1. Dynamical Models For Prices With Distributed Delays

    Directory of Open Access Journals (Sweden)

    Mircea Gabriela

    2015-06-01

    Full Text Available In the present paper we study some models for the price dynamics of a single commodity market. The quantities of supplied and demanded are regarded as a function of time. Nonlinearities in both supply and demand functions are considered. The inventory and the level of inventory are taken into consideration. Due to the fact that the consumer behavior affects commodity demand, and the behavior is influenced not only by the instantaneous price, but also by the weighted past prices, the distributed time delay is introduced. The following kernels are taken into consideration: demand price weak kernel and demand price Dirac kernel. Only one positive equilibrium point is found and its stability analysis is presented. When the demand price kernel is weak, under some conditions of the parameters, the equilibrium point is locally asymptotically stable. When the demand price kernel is Dirac, the existence of the local oscillations is investigated. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. A family of periodic orbits bifurcates from the positive equilibrium point when the time delay passes through a critical value. The last part contains some numerical simulations to illustrate the effectiveness of our results and conclusions.

  2. Coupled nonlinear oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Chandra, J; Scott, A C

    1983-01-01

    Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.

  3. Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems

    Directory of Open Access Journals (Sweden)

    Qi Wang

    2012-01-01

    Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.

  4. Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback

    International Nuclear Information System (INIS)

    Goharrizi, Amin Yazdanpanah; Khaki-Sedigh, Ali; Sepehri, Nariman

    2009-01-01

    A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.

  5. Generalized Nonlinear Yule Models

    Science.gov (United States)

    Lansky, Petr; Polito, Federico; Sacerdote, Laura

    2016-11-01

    With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

  6. Transition among synchronous schemes in coupled nonidentical multiple time delay systems

    International Nuclear Information System (INIS)

    Thang Manh Hoang

    2009-01-01

    We present the transition among possible synchronous schemes in coupled nonidentical multiple time delay systems, i.e., lag, projective-lag, complete, anticipating and projective-anticipating synchronization. The number of nonlinear transforms in the master's equation can be different from that in slave's, and nonlinear transforms can be in various forms. The driving signal is the sum of nonlinearly transformed components of delayed state variable. Moreover, the equation representing for driving signal is constructed exactly so that the difference between the master's and slave's structures is complemented. The sufficient condition for synchronization is considered by the Krasovskii-Lyapunov theory. The specific examples will demonstrate and verify the effectiveness of the proposed models.

  7. Fuzzy delay model based fault simulator for crosstalk delay fault test ...

    Indian Academy of Sciences (India)

    In this paper, a fuzzy delay model based crosstalk delay fault simulator is proposed. As design .... To find the quality of non-robust tests, a fuzzy delay ..... Dubois D and Prade H 1989 Processing Fuzzy temporal knowledge. IEEE Transactions ...

  8. Double Hopf bifurcation in delay differential equations

    Directory of Open Access Journals (Sweden)

    Redouane Qesmi

    2014-07-01

    Full Text Available The paper addresses the computation of elements of double Hopf bifurcation for retarded functional differential equations (FDEs with parameters. We present an efficient method for computing, simultaneously, the coefficients of center manifolds and normal forms, in terms of the original FDEs, associated with the double Hopf singularity up to an arbitrary order. Finally, we apply our results to a nonlinear model with periodic delay. This shows the applicability of the methodology in the study of delay models arising in either natural or technological problems.

  9. Stability and Hopf bifurcation for a business cycle model with expectation and delay

    Science.gov (United States)

    Liu, Xiangdong; Cai, Wenli; Lu, Jiajun; Wang, Yangyang

    2015-08-01

    According to rational expectation hypothesis, the government will take into account the future capital stock in the process of investment decision. By introducing anticipated capital stock into an economic model with investment delay, we construct a mixed functional differential system including delay and advanced variables. The system is converted to the one containing only delay by variable substitution. The equilibrium point of the system is obtained and its dynamical characteristics such as stability, Hopf bifurcation and its stability and direction are investigated by using the related theories of nonlinear dynamics. We carry out some numerical simulations to confirm these theoretical conclusions. The results indicate that both capital stock's anticipation and investment lag are the certain factors leading to the occurrence of cyclical fluctuations in the macroeconomic system. Moreover, the level of economic fluctuation can be dampened to some extent if investment decisions are made by the reasonable short-term forecast on capital stock.

  10. A distributed delay approach for modeling delayed outcomes in pharmacokinetics and pharmacodynamics studies.

    Science.gov (United States)

    Hu, Shuhua; Dunlavey, Michael; Guzy, Serge; Teuscher, Nathan

    2018-04-01

    A distributed delay approach was proposed in this paper to model delayed outcomes in pharmacokinetics and pharmacodynamics studies. This approach was shown to be general enough to incorporate a wide array of pharmacokinetic and pharmacodynamic models as special cases including transit compartment models, effect compartment models, typical absorption models (either zero-order or first-order absorption), and a number of atypical (or irregular) absorption models (e.g., parallel first-order, mixed first-order and zero-order, inverse Gaussian, and Weibull absorption models). Real-life examples were given to demonstrate how to implement distributed delays in Phoenix ® NLME™ 8.0, and to numerically show the advantages of the distributed delay approach over the traditional methods.

  11. Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

    Science.gov (United States)

    Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

    2018-04-01

    The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

  12. Nonlinear models for autoregressive conditional heteroskedasticity

    DEFF Research Database (Denmark)

    Teräsvirta, Timo

    This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation are discu...

  13. Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids

    Science.gov (United States)

    Efimov, Denis; Schiffer, Johannes; Ortega, Romeo

    2016-05-01

    Motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback. The derived theory is applied to two examples. First, the ISS property is established for the model of a nonlinear pendulum and delay-dependent robustness conditions are derived. Second, it is shown that, under certain assumptions, the problem of phase-locking analysis in droop-controlled inverter-based microgrids with delays can be reduced to the stability investigation of the nonlinear pendulum. For this case, corresponding delay-dependent conditions for asymptotic phase-locking are given.

  14. Periodic flows to chaos in time-delay systems

    CERN Document Server

    Luo, Albert C J

    2017-01-01

    This book for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems. Facilitates discovery of analytical solutions of nonlinear time-delay systems; Illustrates bifurcation trees of periodic motions to chaos; Helps readers identify motion complexity and singularity; Explains pro...

  15. Estimation of nonlinearities from pseudodynamic and dynamic responses of bridge structures using the Delay Vector Variance method

    Science.gov (United States)

    Jaksic, Vesna; Mandic, Danilo P.; Karoumi, Raid; Basu, Bidroha; Pakrashi, Vikram

    2016-01-01

    Analysis of the variability in the responses of large structural systems and quantification of their linearity or nonlinearity as a potential non-invasive means of structural system assessment from output-only condition remains a challenging problem. In this study, the Delay Vector Variance (DVV) method is used for full scale testing of both pseudo-dynamic and dynamic responses of two bridges, in order to study the degree of nonlinearity of their measured response signals. The DVV detects the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. The pseudo-dynamic data is obtained from a concrete bridge during repair while the dynamic data is obtained from a steel railway bridge traversed by a train. We show that DVV is promising as a marker in establishing the degree to which a change in the signal nonlinearity reflects the change in the real behaviour of a structure. It is also useful in establishing the sensitivity of instruments or sensors deployed to monitor such changes.

  16. An Epidemic Model of Computer Worms with Time Delay and Variable Infection Rate

    Directory of Open Access Journals (Sweden)

    Yu Yao

    2018-01-01

    Full Text Available With rapid development of Internet, network security issues become increasingly serious. Temporary patches have been put on the infectious hosts, which may lose efficacy on occasions. This leads to a time delay when vaccinated hosts change to susceptible hosts. On the other hand, the worm infection is usually a nonlinear process. Considering the actual situation, a variable infection rate is introduced to describe the spread process of worms. According to above aspects, we propose a time-delayed worm propagation model with variable infection rate. Then the existence condition and the stability of the positive equilibrium are derived. Due to the existence of time delay, the worm propagation system may be unstable and out of control. Moreover, the threshold τ0 of Hopf bifurcation is obtained. The worm propagation system is stable if time delay is less than τ0. When time delay is over τ0, the system will be unstable. In addition, numerical experiments have been performed, which can match the conclusions we deduce. The numerical experiments also show that there exists a threshold in the parameter a, which implies that we should choose appropriate infection rate β(t to constrain worm prevalence. Finally, simulation experiments are carried out to prove the validity of our conclusions.

  17. Mathematical modeling and applications in nonlinear dynamics

    CERN Document Server

    Merdan, Hüseyin

    2016-01-01

    The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

  18. From spiking neuron models to linear-nonlinear models.

    Science.gov (United States)

    Ostojic, Srdjan; Brunel, Nicolas

    2011-01-20

    Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

  19. Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

    Science.gov (United States)

    Si, Wenjie; Dong, Xunde; Yang, Feifei

    2018-03-01

    This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

  20. Leader-following exponential consensus of fractional order nonlinear multi-agents system with hybrid time-varying delay: A heterogeneous impulsive method

    Science.gov (United States)

    Wang, Fei; Yang, Yongqing

    2017-09-01

    In this paper, we study the leader-following exponential consensus of multi-agent system. Each agent in the system is described by nonlinear fractional order differential equation. Both the internal delay and coupling delay are taken into consideration. The heterogeneous impulsive control is used for ensuring the consensus of all agents. Based on Lyapunov function method and matrix analysis, some sufficient conditions for exponential consensus are obtained. Finally, some illustrative examples are given to show the effectiveness of the obtained results.

  1. Finite element model for nonlinear shells of revolution

    International Nuclear Information System (INIS)

    Cook, W.A.

    1979-01-01

    Nuclear material shipping containers have shells of revolution as basic structural components. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Existing models are limited to large displacements, small rotations, and nonlinear materials. The paper presents a finite element model for a nonlinear shell of revolution that will account for large displacements, large strains, large rotations, and nonlinear materials

  2. Modeling delay in genetic networks: from delay birth-death processes to delay stochastic differential equations.

    Science.gov (United States)

    Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Bennett, Matthew R; Josić, Krešimir; Ott, William

    2014-05-28

    Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

  3. Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Bennett, Matthew R. [Department of Biochemistry and Cell Biology, Rice University, Houston, Texas 77204, USA and Institute of Biosciences and Bioengineering, Rice University, Houston, Texas 77005 (United States); Josić, Krešimir [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Department of Biology and Biochemistry, University of Houston, Houston, Texas 77204 (United States)

    2014-05-28

    Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

  4. Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

    International Nuclear Information System (INIS)

    Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William; Bennett, Matthew R.; Josić, Krešimir

    2014-01-01

    Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay

  5. Delayed transitions in non-linear replicator networks: About ghosts and hypercycles

    International Nuclear Information System (INIS)

    Sardanyes, Josep; Sole, Ricard V.

    2007-01-01

    In this paper we analyze delayed transition phenomena associated to extinction thresholds in a mean field model for hypercycles composed of three and four units, respectively. Hence, we extend a previous analysis carried out with the two-membered hypercycle [see Sardanyes J, Sole RV. Ghosts in the origins of life? Int J Bifurcation Chaos 2006;16(9), in press]. The models we analyze show that, after the tangent bifurcation, these hypercycles also leave a ghost in phase space. These ghosts, which actually conserve the dynamical properties of the coalesced coexistence fixed point, delay the flows before hypercycle extinction. In contrast with the two-component hypercycle, both ghosts show a plateau in the delay as φ → 0, thus displacing the power-law dependence to higher values of φ, in which the scaling law is now given by τ ∼ φ β , with β = -1/3 (where τ is the delay and φ = ε - ε c , the parametric distance above the extinction bifurcation point). These results suggest that the presence of the ghost is a general property of hypercycles. Such ghosts actually cause a memory effect which might increase hypercycle survival chances in fluctuating environments

  6. Superspace formulation of new nonlinear sigma models

    International Nuclear Information System (INIS)

    Gates, S.J. Jr.

    1983-07-01

    The superspace formulation of two classes of supersymmetric nonlinear σ-models are presented. Two alternative N=1 superspace formulations are given for the d=2 supersymmetric nonlinear σ-models with Killing vector potentials: (a) formulation uses an active central charge and, (b) formulation uses a spurion superfield without inducing a classical breakdown of supersymmetry. The N=2 vector multiplet is used to construct a new class of d=4 nonlinear σ-models which when reduced to d=2 possess N=4 supersymmetry. Implications of these two classes of nonlinear σ-models for N>=4 superfield supergravity are discussed. (author)

  7. Non-fragile robust stabilization and H{sub {infinity}} control for uncertain stochastic nonlinear time-delay systems

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Jinhui [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: jinhuizhang82@gmail.com; Shi Peng [Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL (United Kingdom); ILSCM, School of Science and Engineering, Victoria University, Melbourne, Vic. 8001 (Australia); School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)], E-mail: pshi@glam.ac.uk; Yang Hongjiu [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: yanghongjiu@gmail.com

    2009-12-15

    This paper deals with the problem of non-fragile robust stabilization and H{sub {infinity}} control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are real time-varying as well as norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such controllers are presented based on the linear matrix inequalities (LMIs) approach. Numerical example is given to illustrate the effectiveness of the developed techniques.

  8. A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay

    International Nuclear Information System (INIS)

    Misra, A.K.; Mishra, S.N.; Pathak, A.L.; Srivastava, P.K.; Chandra, Peeyush

    2013-01-01

    In this paper, a non-linear delay mathematical model for the control of carrier-dependent infectious diseases through insecticides is proposed and analyzed. In the modeling process, it is assumed that disease spreads due to direct contact between susceptibles and infectives as well as through carriers (indirect contact). Further, it is assumed that insecticides are used to kill carriers and the rate of introduction of insecticides is proportional to the density of carriers with some time lag. The model analysis suggests that as delay in using insecticides exceeds some critical value, the system loses its stability and Hopf-bifurcation occurs. The direction, stability and period of the bifurcating periodic solutions arising through Hopf-bifurcation are also analyzed using normal form concept and center manifold theory. Numerical simulation is carried out to confirm the obtained analytical results

  9. Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.

    Science.gov (United States)

    Koch, Gilbert; Krzyzanski, Wojciech; Pérez-Ruixo, Juan Jose; Schropp, Johannes

    2014-08-01

    In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.

  10. A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment

    Directory of Open Access Journals (Sweden)

    Zhu Xiao

    2016-05-01

    Full Text Available In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS, is proposed, which enables vehicle state estimation (VSE with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.

  11. Antiperiodic Solutions for a Kind of Nonlinear Duffing Equations with a Deviating Argument and Time-Varying Delay

    Directory of Open Access Journals (Sweden)

    Changjin Xu

    2014-01-01

    Full Text Available This paper deals with a kind of nonlinear Duffing equation with a deviating argument and time-varying delay. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of antiperiodic solutions for the equation are obtained. Our results are new and complementary to previously known results. An example is given to illustrate the feasibility and effectiveness of our main results.

  12. Forecasting with nonlinear time series models

    DEFF Research Database (Denmark)

    Kock, Anders Bredahl; Teräsvirta, Timo

    In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...... and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...

  13. Fuzzy model-based servo and model following control for nonlinear systems.

    Science.gov (United States)

    Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O

    2009-12-01

    This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.

  14. A delay differential equation model of follicle waves in women.

    Science.gov (United States)

    Panza, Nicole M; Wright, Andrew A; Selgrade, James F

    2016-01-01

    This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.

  15. Identification of nonlinear anelastic models

    International Nuclear Information System (INIS)

    Draganescu, G E; Bereteu, L; Ercuta, A

    2008-01-01

    A useful nonlinear identification technique applied to the anelastic and rheologic models is presented in this paper. First introduced by Feldman, the method is based on the Hilbert transform, and is currently used for identification of the nonlinear vibrations

  16. Relation between nonlinear models and gauge ambiguities

    International Nuclear Information System (INIS)

    Balachandran, A.P.; Ramachandran, R.; Rupertsberger, H.; Skagerstam, B.S.

    1980-01-01

    We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear sigma-models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group). (orig.)

  17. Delay Variation Model with Two Service Queues

    Directory of Open Access Journals (Sweden)

    Filip Rezac

    2010-01-01

    Full Text Available Delay in VoIP technology is very unpleasant issue and therefore a voice packets prioritization must be ensured. To maintain the high call quality a maximum information delivery time from the sender to the recipient is set to 150 ms. This paper focuses on the design of a mathematical model of end-to-end delay of a VoIP connection, in particular on a delay variation. It describes all partial delay components and mechanisms, their generation, facilities and mathematical formulations. A new approach to the delay variation model is presented and its validation has been done by experimention.

  18. Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

    Directory of Open Access Journals (Sweden)

    Zhonghai Guo

    2012-01-01

    Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

  19. Polarization chaos and random bit generation in nonlinear fiber optics induced by a time-delayed counter-propagating feedback loop.

    Science.gov (United States)

    Morosi, J; Berti, N; Akrout, A; Picozzi, A; Guasoni, M; Fatome, J

    2018-01-22

    In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

  20. Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia

    Science.gov (United States)

    Cândea, Doina; Halanay, Andrei; Rǎdulescu, Rodica; Tǎlmaci, Rodica

    2017-01-01

    We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-leukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is to establish which model parameters are the most important in the success or failure of leukemia remission under treatment using a sensitivity analysis of the model parameters. For the most significant parameters of the model which affect the evolution of CML disease during Imatinib treatment we try to estimate the realistic values using some experimental data. For these parameters, steady states are calculated and their stability is analyzed and biologically interpreted.

  1. Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Ping; Song, Heda; Wang, Hong; Chai, Tianyou

    2017-09-01

    Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improve modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.

  2. Physics constrained nonlinear regression models for time series

    International Nuclear Information System (INIS)

    Majda, Andrew J; Harlim, John

    2013-01-01

    A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)

  3. Non-linear finite element modeling

    DEFF Research Database (Denmark)

    Mikkelsen, Lars Pilgaard

    The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...

  4. Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics.

    Science.gov (United States)

    Boulet, Jason; Balasubramaniam, Ramesh; Daffertshofer, Andreas; Longtin, André

    2010-01-28

    We report on experiments and modelling involving the 'visuo-postural control loop' in the upright stance. We experimentally manipulated an artificial delay to the visual feedback during standing, presented at delays ranging from 0 to 1 s in increments of 250 ms. Using stochastic delay differential equations, we explicitly modelled the centre-of-pressure (COP) and centre-of-mass (COM) dynamics with two independent delay terms for vision and proprioception. A novel 'drifting fixed point' hypothesis was used to describe the fluctuations of the COM with the COP being modelled as a faster, corrective process of the COM. The model was in good agreement with the data in terms of probability density functions, power spectral densities, short- and long-term correlations (Hurst exponents) as well the critical time between the two ranges. This journal is © 2010 The Royal Society

  5. Correlations and Non-Linear Probability Models

    DEFF Research Database (Denmark)

    Breen, Richard; Holm, Anders; Karlson, Kristian Bernt

    2014-01-01

    the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....

  6. Non-linear Loudspeaker Unit Modelling

    DEFF Research Database (Denmark)

    Pedersen, Bo Rohde; Agerkvist, Finn T.

    2008-01-01

    Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....

  7. Local stability and Hopf bifurcation in small-world delayed networks

    International Nuclear Information System (INIS)

    Li Chunguang; Chen Guanrong

    2004-01-01

    The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis

  8. Local stability and Hopf bifurcation in small-world delayed networks

    Energy Technology Data Exchange (ETDEWEB)

    Li Chunguang E-mail: cgli@uestc.edu.cn; Chen Guanrong E-mail: gchen@ee.cityu.edu.hk

    2004-04-01

    The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis.

  9. A robust control strategy for a class of distributed network with transmission delays

    DEFF Research Database (Denmark)

    Vahid Naghavi, S.; A. Safavi, A.; Khooban, Mohammad Hassan

    2016-01-01

    Purpose The purpose of this paper is to concern the design of a robust model predictive controller for distributed networked systems with transmission delays. Design/methodology/approach The overall system is composed of a number of interconnected nonlinear subsystems with time-varying transmission...... as an optimization problem of a “worst-case” objective function over an infinite moving horizon. Findings The aim is to propose control synthesis approach that depends on nonlinearity and time varying delay characteristics. The MPC problem is represented in a time varying delayed state feedback structure....... Then the synthesis sufficient condition is provided in the form of a linear matrix inequality (LMI) optimization and is solved online at each time instant. In the rest, an LMI-based decentralized observer-based robust model predictive control strategy is proposed. Originality/value The authors develop RMPC...

  10. Fractional-Order Control of a Nonlinear Time-Delay System: Case Study in Oxygen Regulation in the Heart-Lung Machine

    Directory of Open Access Journals (Sweden)

    S. J. Sadati

    2012-01-01

    Full Text Available A fractional-order controller will be proposed to regulate the inlet oxygen into the heart-lung machine. An analytical approach will be explained to satisfy some requirements together with practical implementation of some restrictions for the first time. Primarily a nonlinear single-input single-output (SISO time-delay model which was obtained previously in the literature is introduced for the oxygen generation process in the heart-lung machine system and we will complete it by adding some new states to control it. Thereafter, the system is linearized using the state feedback linearization approach to find a third-order time-delay dynamics. Consequently classical PID and fractional order controllers are gained to assess the quality of the proposed technique. A set of optimal parameters of those controllers are achieved through the genetic algorithm optimization procedure through minimizing a cost function. Our design method focuses on minimizing some famous performance criterions such as IAE, ISE, and ITSE. In the genetic algorithm, the controller parameters are chosen as a random population. The best relevant values are achieved by reducing the cost function. A time-domain simulation signifies the performance of controller with respect to a traditional optimized PID controller.

  11. Linear time delay methods and stability analyses of the human spine. Effects of neuromuscular reflex response.

    Science.gov (United States)

    Franklin, Timothy C; Granata, Kevin P; Madigan, Michael L; Hendricks, Scott L

    2008-08-01

    Linear stability methods were applied to a biomechanical model of the human musculoskeletal spine to investigate effects of reflex gain and reflex delay on stability. Equations of motion represented a dynamic 18 degrees-of-freedom rigid-body model with time-delayed reflexes. Optimal muscle activation levels were identified by minimizing metabolic power with the constraints of equilibrium and stability with zero reflex time delay. Muscle activation levels and associated muscle forces were used to find the delay margin, i.e., the maximum reflex delay for which the system was stable. Results demonstrated that stiffness due to antagonistic co-contraction necessary for stability declined with increased proportional reflex gain. Reflex delay limited the maximum acceptable proportional reflex gain, i.e., long reflex delay required smaller maximum reflex gain to avoid instability. As differential reflex gain increased, there was a small increase in acceptable reflex delay. However, differential reflex gain with values near intrinsic damping caused the delay margin to approach zero. Forward-dynamic simulations of the fully nonlinear time-delayed system verified the linear results. The linear methods accurately found the delay margin below which the nonlinear system was asymptotically stable. These methods may aid future investigations in the role of reflexes in musculoskeletal stability.

  12. Robust control of time-delay chaotic systems

    International Nuclear Information System (INIS)

    Hua Changchun; Guan Xinping

    2003-01-01

    Robust control problem of nonlinear time-delay chaotic systems is investigated. For such uncertain systems, we propose adaptive feedback controller and novel nonlinear feedback controller. They are both independent of the time delay and can render the corresponding closed-loop systems globally uniformly ultimately bounded stable. The simulations on controlling logistic system are made and the results show the controllers are feasible

  13. Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay

    International Nuclear Information System (INIS)

    Ding Yuting; Jiang Weihua; Wang Hongbin

    2012-01-01

    Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.

  14. Modeling of Volatility with Non-linear Time Series Model

    OpenAIRE

    Kim Song Yon; Kim Mun Chol

    2013-01-01

    In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.

  15. A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity

    Science.gov (United States)

    Fan, Kuangang; Zhang, Yan; Gao, Shujing; Wei, Xiang

    2017-09-01

    A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R0 is obtained. We show that if R0 extinct with probability one, whereas if R0 > 1, then the system remains permanent in the mean.

  16. Comparing coefficients of nested nonlinear probability models

    DEFF Research Database (Denmark)

    Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders

    2011-01-01

    In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...

  17. Lie group classification of first-order delay ordinary differential equations

    Science.gov (United States)

    Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

    2018-05-01

    A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

  18. Disequilibrium dynamics in a Keynesian model with time delays

    Science.gov (United States)

    Gori, Luca; Guerrini, Luca; Sodini, Mauro

    2018-05-01

    The aim of this research is to analyse a Keynesian goods market closed economy by considering a continuous-time setup with fixed delays. The work compares dynamic results based on linear and nonlinear adjustment mechanisms through which the aggregate supply (production) reacts to a disequilibrium in the goods market and consumption depends on income at a preceding date. Both analytical and geometrical (stability switching curves) techniques are used to characterise the stability properties of the stationary equilibrium.

  19. Nonlinear Control of Heartbeat Models

    Directory of Open Access Journals (Sweden)

    Witt Thanom

    2011-02-01

    Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.

  20. Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization

    International Nuclear Information System (INIS)

    Sun Jitao; Han Qinglong; Jiang Xiefu

    2008-01-01

    This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results

  1. Nonlinear dynamics and complexity

    CERN Document Server

    Luo, Albert; Fu, Xilin

    2014-01-01

    This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

  2. Pull-in instability tuning in imperfect nonlinear circular microplates under electrostatic actuation

    Energy Technology Data Exchange (ETDEWEB)

    Jallouli, A.; Kacem, N., E-mail: najib.kacem@univ-fcomte.fr; Bourbon, G.; Le Moal, P.; Walter, V.; Lardies, J.

    2016-12-01

    Highlights: • Dynamic range improvement of electrostatically actuated circular microplates. • Pull-in instability tuning based on geometric nonlinearity and imperfections. • Predictive computational model for the nonlinear behavior of circular microplates. - Abstract: Dynamic range improvement based on geometric nonlinearity and initial deflection is demonstrated with imperfect circular microplates under electrostatic actuation. Depending on design parameters, we prove how the von Kármán nonlinearity and the plate imperfections lead to a significant delay in pull-in occurrence. These promising results open the way towards an accurate identification of static parameters of circular microplates and the development of a predictive model for the nonlinear dynamics of imperfect capacitive micromachined ultrasonic transducers.

  3. An adaptive robust controller for time delay maglev transportation systems

    Science.gov (United States)

    Milani, Reza Hamidi; Zarabadipour, Hassan; Shahnazi, Reza

    2012-12-01

    For engineering systems, uncertainties and time delays are two important issues that must be considered in control design. Uncertainties are often encountered in various dynamical systems due to modeling errors, measurement noises, linearization and approximations. Time delays have always been among the most difficult problems encountered in process control. In practical applications of feedback control, time delay arises frequently and can severely degrade closed-loop system performance and in some cases, drives the system to instability. Therefore, stability analysis and controller synthesis for uncertain nonlinear time-delay systems are important both in theory and in practice and many analytical techniques have been developed using delay-dependent Lyapunov function. In the past decade the magnetic and levitation (maglev) transportation system as a new system with high functionality has been the focus of numerous studies. However, maglev transportation systems are highly nonlinear and thus designing controller for those are challenging. The main topic of this paper is to design an adaptive robust controller for maglev transportation systems with time-delay, parametric uncertainties and external disturbances. In this paper, an adaptive robust control (ARC) is designed for this purpose. It should be noted that the adaptive gain is derived from Lyapunov-Krasovskii synthesis method, therefore asymptotic stability is guaranteed.

  4. Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay

    Science.gov (United States)

    Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai

    2016-08-01

    In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.

  5. Geometric methods of global attraction in systems of delay differential equations

    Science.gov (United States)

    El-Morshedy, Hassan A.; Ruiz-Herrera, Alfonso

    2017-11-01

    In this paper we deduce criteria of global attraction in systems of delay differential equations. Our methodology is new and consists in "dominating" the nonlinear terms of the system by a scalar function and then studying some dynamical properties of that function. One of the crucial benefits of our approach is that we obtain delay-dependent results of global attraction that cover the best delay-independent conditions. We apply our results in a gene regulatory model and the classical Nicholson's blowfly equation with patch structure.

  6. Nonlinear structural mechanics theory, dynamical phenomena and modeling

    CERN Document Server

    Lacarbonara, Walter

    2013-01-01

    Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

  7. Explicit Nonlinear Model Predictive Control Theory and Applications

    CERN Document Server

    Grancharova, Alexandra

    2012-01-01

    Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

  8. Delayed nonlinear cournot and bertrand dynamics with product differentiation.

    Science.gov (United States)

    Matsumoto, Akio; Szidarovszky, Ferenc

    2007-07-01

    Dynamic duopolies will be examined with product differentiation and isoelastic price functions. We will first prove that under realistic conditions the equilibrium is always locally asymptotically stable. The stability can however be lost if the firms use delayed information in forming their best responses. Stability conditions are derived in special cases, and simulation results illustrate the complexity of the dynamism of the systems. Both price and quantity adjusting models are discussed.

  9. Analysis of nonlinear systems using ARMA [autoregressive moving average] models

    International Nuclear Information System (INIS)

    Hunter, N.F. Jr.

    1990-01-01

    While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs

  10. Localization of Non-Linearly Modeled Autonomous Mobile Robots Using Out-of-Sequence Measurements

    Directory of Open Access Journals (Sweden)

    Jesus M. de la Cruz

    2012-02-01

    Full Text Available This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.

  11. Nonlinear State Space Modeling and System Identification for Electrohydraulic Control

    Directory of Open Access Journals (Sweden)

    Jun Yan

    2013-01-01

    Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

  12. Hopf bifurcation of an (n + 1) -neuron bidirectional associative memory neural network model with delays.

    Science.gov (United States)

    Xiao, Min; Zheng, Wei Xing; Cao, Jinde

    2013-01-01

    Recent studies on Hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two, three, four, five, or six neurons. It is well known that neural networks are complex and large-scale nonlinear dynamical systems, so the dynamics of the delayed neural networks are very rich and complicated. Although discussing the dynamics of networks with a few neurons may help us to understand large-scale networks, there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large-scale networks. In this paper, a general delayed bidirectional associative memory neural network model with n + 1 neurons is considered. By analyzing the associated characteristic equation, the local stability of the trivial steady state is examined, and then the existence of the Hopf bifurcation at the trivial steady state is established. By applying the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution. Furthermore, the paper highlights situations where the Hopf bifurcations are particularly critical, in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections. It is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons. Numerical simulations are carried out to illustrate the main results.

  13. Nonlinear dynamics analysis of a modified optically injected semiconductor lasers model

    International Nuclear Information System (INIS)

    Chu Yandong; Li Xianfeng; Zhang Jiangang; Chang Yingxiang

    2009-01-01

    In this paper, a new nonlinear autonomous system that was introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or numerically, such as Poincare mapping, Lyapunov exponents, fractal dimension, continuous power spectrum and so forth. Furthermore, the coexistence of different attractors is discovered on the Poincare maps. Meanwhile, chaotic oscillation of this system is converted into a stable periodic orbit with the method of time-delayed feedback, which demonstrated by numerical simulations and the robustness of this method is proved.

  14. Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

    DEFF Research Database (Denmark)

    Lee, Kyo-Beum; Blaabjerg, Frede

    2004-01-01

    This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...

  15. NONLINEAR PLANT PIECEWISE-CONTINUOUS MODEL MATRIX PARAMETERS ESTIMATION

    Directory of Open Access Journals (Sweden)

    Roman L. Leibov

    2017-09-01

    Full Text Available This paper presents a nonlinear plant piecewise-continuous model matrix parameters estimation technique using nonlinear model time responses and random search method. One of piecewise-continuous model application areas is defined. The results of proposed approach application for aircraft turbofan engine piecewisecontinuous model formation are presented

  16. 4th International Conference on Structural Nonlinear Dynamics and Diagnosis

    CERN Document Server

    2018-01-01

    This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...

  17. Predictor feedback for delay systems implementations and approximations

    CERN Document Server

    Karafyllis, Iasson

    2017-01-01

    This monograph bridges the gap between the nonlinear predictor as a concept and as a practical tool, presenting a complete theory of the application of predictor feedback to time-invariant, uncertain systems with constant input delays and/or measurement delays. It supplies several methods for generating the necessary real-time solutions to the systems’ nonlinear differential equations, which the authors refer to as approximate predictors. Predictor feedback for linear time-invariant (LTI) systems is presented in Part I to provide a solid foundation on the necessary concepts, as LTI systems pose fewer technical difficulties than nonlinear systems. Part II extends all of the concepts to nonlinear time-invariant systems. Finally, Part III explores extensions of predictor feedback to systems described by integral delay equations and to discrete-time systems. The book’s core is the design of control and observer algorithms with which global stabilization, guaranteed in the previous literature with idealized (b...

  18. Study of the nonlinear imperfect software debugging model

    International Nuclear Information System (INIS)

    Wang, Jinyong; Wu, Zhibo

    2016-01-01

    In recent years there has been a dramatic proliferation of research on imperfect software debugging phenomena. Software debugging is a complex process and is affected by a variety of factors, including the environment, resources, personnel skills, and personnel psychologies. Therefore, the simple assumption that debugging is perfect is inconsistent with the actual software debugging process, wherein a new fault can be introduced when removing a fault. Furthermore, the fault introduction process is nonlinear, and the cumulative number of nonlinearly introduced faults increases over time. Thus, this paper proposes a nonlinear, NHPP imperfect software debugging model in consideration of the fact that fault introduction is a nonlinear process. The fitting and predictive power of the NHPP-based proposed model are validated through related experiments. Experimental results show that this model displays better fitting and predicting performance than the traditional NHPP-based perfect and imperfect software debugging models. S-confidence bounds are set to analyze the performance of the proposed model. This study also examines and discusses optimal software release-time policy comprehensively. In addition, this research on the nonlinear process of fault introduction is significant given the recent surge of studies on software-intensive products, such as cloud computing and big data. - Highlights: • Fault introduction is a nonlinear changing process during the debugging phase. • The assumption that the process of fault introduction is nonlinear is credible. • Our proposed model can better fit and accurately predict software failure behavior. • Research on fault introduction case is significant to software-intensive products.

  19. Heterotic sigma models and non-linear strings

    International Nuclear Information System (INIS)

    Hull, C.M.

    1986-01-01

    The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)

  20. Identifying time-delayed gene regulatory networks via an evolvable hierarchical recurrent neural network.

    Science.gov (United States)

    Kordmahalleh, Mina Moradi; Sefidmazgi, Mohammad Gorji; Harrison, Scott H; Homaifar, Abdollah

    2017-01-01

    The modeling of genetic interactions within a cell is crucial for a basic understanding of physiology and for applied areas such as drug design. Interactions in gene regulatory networks (GRNs) include effects of transcription factors, repressors, small metabolites, and microRNA species. In addition, the effects of regulatory interactions are not always simultaneous, but can occur after a finite time delay, or as a combined outcome of simultaneous and time delayed interactions. Powerful biotechnologies have been rapidly and successfully measuring levels of genetic expression to illuminate different states of biological systems. This has led to an ensuing challenge to improve the identification of specific regulatory mechanisms through regulatory network reconstructions. Solutions to this challenge will ultimately help to spur forward efforts based on the usage of regulatory network reconstructions in systems biology applications. We have developed a hierarchical recurrent neural network (HRNN) that identifies time-delayed gene interactions using time-course data. A customized genetic algorithm (GA) was used to optimize hierarchical connectivity of regulatory genes and a target gene. The proposed design provides a non-fully connected network with the flexibility of using recurrent connections inside the network. These features and the non-linearity of the HRNN facilitate the process of identifying temporal patterns of a GRN. Our HRNN method was implemented with the Python language. It was first evaluated on simulated data representing linear and nonlinear time-delayed gene-gene interaction models across a range of network sizes and variances of noise. We then further demonstrated the capability of our method in reconstructing GRNs of the Saccharomyces cerevisiae synthetic network for in vivo benchmarking of reverse-engineering and modeling approaches (IRMA). We compared the performance of our method to TD-ARACNE, HCC-CLINDE, TSNI and ebdbNet across different network

  1. Assessment of tropospheric delay mapping function models in Egypt: Using PTD database model

    Science.gov (United States)

    Abdelfatah, M. A.; Mousa, Ashraf E.; El-Fiky, Gamal S.

    2018-06-01

    For space geodetic measurements, estimates of tropospheric delays are highly correlated with site coordinates and receiver clock biases. Thus, it is important to use the most accurate models for the tropospheric delay to reduce errors in the estimates of the other parameters. Both the zenith delay value and mapping function should be assigned correctly to reduce such errors. Several mapping function models can treat the troposphere slant delay. The recent models were not evaluated for the Egyptian local climate conditions. An assessment of these models is needed to choose the most suitable one. The goal of this paper is to test the quality of global mapping function which provides high consistency with precise troposphere delay (PTD) mapping functions. The PTD model is derived from radiosonde data using ray tracing, which consider in this paper as true value. The PTD mapping functions were compared, with three recent total mapping functions model and another three separate dry and wet mapping function model. The results of the research indicate that models are very close up to zenith angle 80°. Saastamoinen and 1/cos z model are behind accuracy. Niell model is better than VMF model. The model of Black and Eisner is a good model. The results also indicate that the geometric range error has insignificant effect on slant delay and the fluctuation of azimuth anti-symmetric is about 1%.

  2. Nonlinear distortion in wireless systems modeling and simulation with Matlab

    CERN Document Server

    Gharaibeh, Khaled M

    2011-01-01

    This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems

  3. Modeling Directional Selectivity Using Self-Organizing Delay-Aadaptation Maps

    OpenAIRE

    Tversky, Mr. Tal; Miikkulainen, Dr. Risto

    2002-01-01

    Using a delay adaptation learning rule, we model the activity-dependent development of directionally selective cells in the primary visual cortex. Based on input stimuli, a learning rule shifts delays to create synchronous arrival of spikes at cortical cells. As a result, delays become tuned creating a smooth cortical map of direction selectivity. This result demonstrates how delay adaption can serve as a powerful abstraction for modeling temporal learning in the brain.

  4. The Aviation System Analysis Capability Airport Capacity and Delay Models

    Science.gov (United States)

    Lee, David A.; Nelson, Caroline; Shapiro, Gerald

    1998-01-01

    The ASAC Airport Capacity Model and the ASAC Airport Delay Model support analyses of technologies addressing airport capacity. NASA's Aviation System Analysis Capability (ASAC) Airport Capacity Model estimates the capacity of an airport as a function of weather, Federal Aviation Administration (FAA) procedures, traffic characteristics, and the level of technology available. Airport capacity is presented as a Pareto frontier of arrivals per hour versus departures per hour. The ASAC Airport Delay Model allows the user to estimate the minutes of arrival delay for an airport, given its (weather dependent) capacity. Historical weather observations and demand patterns are provided by ASAC as inputs to the delay model. The ASAC economic models can translate a reduction in delay minutes into benefit dollars.

  5. Bifurcation analysis of delay-induced periodic oscillations

    NARCIS (Netherlands)

    Green, K.

    2010-01-01

    In this paper we consider a generic differential equation with a cubic nonlinearity and delay. This system, in the absence of delay, is known to undergo an oscillatory instability. The addition of the delay is shown to result in the creation of a number of periodic solutions with constant amplitude

  6. Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

    Science.gov (United States)

    Maillou, Balbine; Lotton, Pierrick; Novak, Antonin; Simon, Laurent

    2018-03-01

    Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

  7. Discrete-time nonlinear sliding mode controller

    African Journals Online (AJOL)

    user

    Keywords: Discrete-time delay system, Sliding mode control, nonlinear sliding ... of engineering systems such as chemical process control, delay in the actuator ...... instrumentation from Motilal Nehru National Institute of Technology (MNNIT),.

  8. Direct approach for solving nonlinear evolution and two-point

    Indian Academy of Sciences (India)

    Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

  9. Analysis of a Dynamical Cournot Duopoly Game with Distributed Time Delay

    Directory of Open Access Journals (Sweden)

    SÎrghi Nicoleta

    2015-03-01

    Full Text Available The aim of the paper is to analyze the dynamic model of the Cournot duopoly game with bounded rationality associated to two firms. We consider the cost function of the first firm as nonlinear and for the second firm as linear. The players do not have a complete knowledge of the market and they follow a bounded rationality adjustment process based on the estimation of the marginal profit. Also, the distributed time delay is introduced, because the decisions at the current time depend on the average past decisions. The mathematical model is described by a distributed delay differential system with two nonlinear equations. The study for the local stability of the Nash equilibrium point is carried out in the case of two types of kernels: weak (exponential and Dirac. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. The delays are considered as bifurcation parameters. In some conditions of the parameters of the model, we have proved that a family of periodic solutions bifurcates from the equilibrium point when the bifurcation parameter passes through a critical value. Numerical simulations are performed to illustrate the effectiveness of our results. Finally, conclusions and future researches are provided.

  10. Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift

    Directory of Open Access Journals (Sweden)

    Gemechis File

    2012-01-01

    Full Text Available We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .

  11. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

    Science.gov (United States)

    Benhammouda, Brahim; Vazquez-Leal, Hector

    2016-01-01

    This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

  12. Model reduction of nonlinear systems subject to input disturbances

    KAUST Repository

    Ndoye, Ibrahima

    2017-07-10

    The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.

  13. Non-linear Growth Models in Mplus and SAS

    Science.gov (United States)

    Grimm, Kevin J.; Ram, Nilam

    2013-01-01

    Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

  14. Global output feedback control for a class of high-order feedforward nonlinear systems with input delay.

    Science.gov (United States)

    Zha, Wenting; Zhai, Junyong; Fei, Shumin

    2013-07-01

    This paper investigates the problem of output feedback stabilization for a class of high-order feedforward nonlinear systems with time-varying input delay. First, a scaling gain is introduced into the system under a set of coordinate transformations. Then, the authors construct an observer and controller to make the nominal system globally asymptotically stable. Based on homogeneous domination approach and Lyapunov-Krasovskii functional, it is shown that the closed-loop system can be rendered globally asymptotically stable by the scaling gain. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

  15. A novel delay-dependent criterion for delayed neural networks of neutral type

    International Nuclear Information System (INIS)

    Lee, S.M.; Kwon, O.M.; Park, Ju H.

    2010-01-01

    This Letter considers a robust stability analysis method for delayed neural networks of neutral type. By constructing a new Lyapunov functional, a novel delay-dependent criterion for the stability is derived in terms of LMIs (linear matrix inequalities). A less conservative stability criterion is derived by using nonlinear properties of the activation function of the neural networks. Two numerical examples are illustrated to show the effectiveness of the proposed method.

  16. Modeling endocrine regulation of the menstrual cycle using delay differential equations.

    Science.gov (United States)

    Harris, Leona A; Selgrade, James F

    2014-11-01

    This article reviews an effective mathematical procedure for modeling hormonal regulation of the menstrual cycle of adult women. The procedure captures the effects of hormones secreted by several glands over multiple time scales. The specific model described here consists of 13 nonlinear, delay, differential equations with 44 parameters and correctly predicts blood levels of ovarian and pituitary hormones found in the biological literature for normally cycling women. In addition to this normal cycle, the model exhibits another stable cycle which may describe a biologically feasible "abnormal" condition such as polycystic ovarian syndrome. Model simulations illustrate how one cycle can be perturbed to the other cycle. Perturbations due to the exogenous administration of each ovarian hormone are examined. This model may be used to test the effects of hormone therapies on abnormally cycling women as well as the effects of exogenous compounds on normally cycling women. Sensitive parameters are identified and bifurcations in model behavior with respect to parameter changes are discussed. Modeling various aspects of menstrual cycle regulation should be helpful in predicting successful hormone therapies, in studying the phenomenon of cycle synchronization and in understanding many factors affecting the aging of the female reproductive endocrine system. Copyright © 2014 Elsevier Inc. All rights reserved.

  17. Model of anisotropic nonlinearity in self-defocusing photorefractive media.

    Science.gov (United States)

    Barsi, C; Fleischer, J W

    2015-09-21

    We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.

  18. Advances and applications in nonlinear control systems

    CERN Document Server

    Volos, Christos

    2016-01-01

    The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design proce...

  19. Climate models with delay differential equations.

    Science.gov (United States)

    Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire M

    2017-11-01

    A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be described and not the processes themselves. This is true for some climate systems, whose dynamics are driven in part by delayed feedback loops associated with transport times of mass or energy from one location of the globe to another. The infinite-dimensional nature of DDEs allows them to be sufficiently complex to reproduce realistic dynamics accurately with a small number of variables and parameters. In this paper, we review how DDEs have been used to model climate systems at a conceptual level. Most studies of DDE climate models have focused on gaining insights into either the global energy balance or the fundamental workings of the El Niño Southern Oscillation (ENSO) system. For example, studies of DDEs have led to proposed mechanisms for the interannual oscillations in sea-surface temperature that is characteristic of ENSO, the irregular behaviour that makes ENSO difficult to forecast and the tendency of El Niño events to occur near Christmas. We also discuss the tools used to analyse such DDE models. In particular, the recent development of continuation software for DDEs makes it possible to explore large regions of parameter space in an efficient manner in order to provide a "global picture" of the possible dynamics. We also point out some directions for future research, including the incorporation of non-constant delays, which we believe could improve the descriptive power of DDE climate models.

  20. Climate models with delay differential equations

    Science.gov (United States)

    Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire M.

    2017-11-01

    A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be described and not the processes themselves. This is true for some climate systems, whose dynamics are driven in part by delayed feedback loops associated with transport times of mass or energy from one location of the globe to another. The infinite-dimensional nature of DDEs allows them to be sufficiently complex to reproduce realistic dynamics accurately with a small number of variables and parameters. In this paper, we review how DDEs have been used to model climate systems at a conceptual level. Most studies of DDE climate models have focused on gaining insights into either the global energy balance or the fundamental workings of the El Niño Southern Oscillation (ENSO) system. For example, studies of DDEs have led to proposed mechanisms for the interannual oscillations in sea-surface temperature that is characteristic of ENSO, the irregular behaviour that makes ENSO difficult to forecast and the tendency of El Niño events to occur near Christmas. We also discuss the tools used to analyse such DDE models. In particular, the recent development of continuation software for DDEs makes it possible to explore large regions of parameter space in an efficient manner in order to provide a "global picture" of the possible dynamics. We also point out some directions for future research, including the incorporation of non-constant delays, which we believe could improve the descriptive power of DDE climate models.

  1. Nonlinear Robust Observer-Based Fault Detection for Networked Suspension Control System of Maglev Train

    Directory of Open Access Journals (Sweden)

    Yun Li

    2013-01-01

    Full Text Available A fault detection approach based on nonlinear robust observer is designed for the networked suspension control system of Maglev train with random induced time delay. First, considering random bounded time-delay and external disturbance, the nonlinear model of the networked suspension control system is established. Then, a nonlinear robust observer is designed using the input of the suspension gap. And the estimate error is proved to be bounded with arbitrary precision by adopting an appropriate parameter. When sensor faults happen, the residual between the real states and the observer outputs indicates which kind of sensor failures occurs. Finally, simulation results using the actual parameters of CMS-04 maglev train indicate that the proposed method is effective for maglev train.

  2. Proposition of delay model for signalized intersections with queueing theory analytical models usage

    Directory of Open Access Journals (Sweden)

    Grzegorz SIERPIŃSKI

    2007-01-01

    Full Text Available Time delay on intersections is a very important transport problem. Thearticle includes a proposition of time delay model. Variance of service times is considered by used average waiting time in queue for queuing system with compressed queuing processes usage as a part of proposed time delays model.

  3. Nonlinear model predictive control theory and algorithms

    CERN Document Server

    Grüne, Lars

    2017-01-01

    This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...

  4. Nonlinear resonance in Duffing oscillator with fixed and integrative ...

    Indian Academy of Sciences (India)

    We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...

  5. Nonlinear resonance in Duffing oscillator with fixed and integrative ...

    Indian Academy of Sciences (India)

    2012-03-02

    Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...

  6. Parameter Estimation of Nonlinear Models in Forestry.

    OpenAIRE

    Fekedulegn, Desta; Mac Siúrtáin, Máirtín Pádraig; Colbert, Jim J.

    1999-01-01

    Partial derivatives of the negative exponential, monomolecular, Mitcherlich, Gompertz, logistic, Chapman-Richards, von Bertalanffy, Weibull and the Richard’s nonlinear growth models are presented. The application of these partial derivatives in estimating the model parameters is illustrated. The parameters are estimated using the Marquardt iterative method of nonlinear regression relating top height to age of Norway spruce (Picea abies L.) from the Bowmont Norway Spruce Thinnin...

  7. Identification of the Response of a Controlled Building Structure Subjected to Seismic Load by Using Nonlinear System Models

    Directory of Open Access Journals (Sweden)

    Mosbeh R. Kaloop

    2016-10-01

    Full Text Available The present study investigates the prediction efficiency of nonlinear system-identification models, in assessing the behavior of a coupled structure-passive vibration controller. Two system-identification models, including Nonlinear AutoRegresive with eXogenous inputs (NARX and adaptive neuro-fuzzy inference system (ANFIS, are used to model the behavior of an experimentally scaled three-story building incorporated with a tuned mass damper (TMD subjected to seismic loads. The experimental study is performed to generate the input and output data sets for training and testing the designed models. The parameters of root-mean-squared error, mean absolute error and determination coefficient statistics are used to compare the performance of the aforementioned models. A TMD controller system works efficiently to mitigate the structural vibration. The results revealed that the NARX and ANFIS models could be used to identify the response of a controlled structure. The parameters of both two time-delays of the structure response and the seismic load were proven to be effective tools in identifying the performance of the models. A comparison based on the parametric evaluation of the two methods showed that the NARX model outperforms the ANFIS model in identifying structures response.

  8. A Simple Model for Nonlinear Confocal Ultrasonic Beams

    Science.gov (United States)

    Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

    2007-01-01

    A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

  9. CALCULUS FROM THE PAST: MULTIPLE DELAY SYSTEMS ARISING IN CANCER CELL MODELLING

    KAUST Repository

    WAKE, G. C.; BYRNE, H. M.

    2013-01-01

    Nonlocal calculus is often overlooked in the mathematics curriculum. In this paper we present an interesting new class of nonlocal problems that arise from modelling the growth and division of cells, especially cancer cells, as they progress through the cell cycle. The cellular biomass is assumed to be unstructured in size or position, and its evolution governed by a time-dependent system of ordinary differential equations with multiple time delays. The system is linear and taken to be autonomous. As a result, it is possible to reduce its solution to that of a nonlinear matrix eigenvalue problem. This method is illustrated by considering case studies, including a model of the cell cycle developed recently by Simms, Bean and Koeber. The paper concludes by explaining how asymptotic expressions for the distribution of cells across the compartments can be determined and used to assess the impact of different chemotherapeutic agents. Copyright © 2013 Australian Mathematical Society.

  10. Methodology for Analysis, Modeling and Simulation of Airport Gate-waiting Delays

    Science.gov (United States)

    Wang, Jianfeng

    availability. Analysis of the worst days at six major airports in the summer of 2007 indicates that major gate-waiting delays are primarily due to operational disruptions---specifically, extended gate occupancy time, reduced gate availability and higher-than-scheduled arrival rate (usually due to arrival delay). Major gate-waiting delays are not a result of over-scheduling. The second part of this dissertation presents a simulation model to evaluate the impact of gate operational disruptions and gate-waiting-delay mitigation strategies, including building new gates, implementing common gates, using overnight off-gate parking and adopting self-docking gates. Simulation results show the following effects of disruptions: (i) The impact of arrival delay in a time window (e.g. 7 pm to 9 pm) on gate-waiting delay is bounded. (ii) The impact of longer-than-scheduled gate-occupancy times in a time window on gate-waiting delay can be unbounded and gate-waiting delay can increase linearly as the disruption level increases. (iii) Small reductions in gate availability have a small impact on gate-waiting delay due to slack gate capacity, while larger reductions have a non-linear impact as slack gate capacity is used up. Simulation results show the following effects of mitigation strategies: (i) Implementing common gates is an effective mitigation strategy, especially for airports with a flight schedule not dominated by one carrier, such as LGA. (ii) The overnight off-gate rule is effective in mitigating gate-waiting delay for flights stranded overnight following departure cancellations. This is especially true at airports where the gate utilization is at maximum overnight, such as LGA and DFW. The overnight off-gate rule can also be very effective to mitigate gate-waiting delay due to operational disruptions in evenings. (iii) Self-docking gates are effective in mitigating gate-waiting delay due to reduced gate availability.

  11. A Cucker--Smale Model with Noise and Delay

    KAUST Repository

    Erban, Radek

    2016-08-09

    A generalization of the Cucker-Smale model for collective animal behavior is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modeling: (i) stochasticity (imperfections) of individual behavior and (ii) delayed responses of individuals to signals in their environment. Sufficient conditions for flocking for the generalized Cucker-Smale model are derived by using a suitable Lyapunov functional. As a by-product, a new result regarding the asymptotic behavior of delayed geometric Brownian motion is obtained. In the second part of the paper, results of systematic numerical simulations are presented. They not only illustrate the analytical results, but hint at a somehow surprising behavior

  12. A Cucker--Smale Model with Noise and Delay

    KAUST Repository

    Erban, Radek; Haskovec, Jan; Sun, Yongzheng

    2016-01-01

    A generalization of the Cucker-Smale model for collective animal behavior is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modeling: (i) stochasticity (imperfections) of individual behavior and (ii) delayed responses of individuals to signals in their environment. Sufficient conditions for flocking for the generalized Cucker-Smale model are derived by using a suitable Lyapunov functional. As a by-product, a new result regarding the asymptotic behavior of delayed geometric Brownian motion is obtained. In the second part of the paper, results of systematic numerical simulations are presented. They not only illustrate the analytical results, but hint at a somehow surprising behavior

  13. Nonlinear flow model for well production in an underground formation

    Directory of Open Access Journals (Sweden)

    J. C. Guo

    2013-05-01

    Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

  14. Nonlinear Dynamics of Ultrashort Long-Range Surface Plasmon Polariton Pulses in Gold Strip Waveguides

    DEFF Research Database (Denmark)

    Lysenko, Oleg; Bache, Morten; Olivier, Nicolas

    2016-01-01

    We study experimentally and theoretically nonlinear propagation of ultrashort long-range surface plasmon polaritons in gold strip waveguides. The nonlinear absorption of the plasmonic modes in the waveguides is measured with femtosecond pulses revealing a strong dependence of the third......-order nonlinear susceptibility of the gold core on the pulse duration and layer thickness. A comprehensive model for the pulse duration dependence of the third-order nonlinear susceptibility is developed on the basis of the nonlinear Schrödinger equation for plasmonic mode propagation in the waveguides....... The model accounts for the intrinsic delayed (noninstantaneous) nonlinearity of free electrons of gold as well as the thickness of the gold film and is experimentally verified. The obtained results are important for the development of active plasmonic and nanophotonic components....

  15. Dynamics and control of a financial system with time-delayed feedbacks

    International Nuclear Information System (INIS)

    Chen, W.-C.

    2008-01-01

    Complex behaviors in a financial system with time-delayed feedbacks are discussed in this study via numerical modeling. The system shows complex dynamics such as periodic, quasi-periodic, and chaotic behaviors. Both period doubling and inverse period doubling routes were found in this system. This paper also shows that the attractor merging crisis is a fundamental feature of nonlinear financial systems with time-delayed feedbacks. Control of the deterministic chaos in the financial system can be realized using Pyragas feedbacks

  16. Anti-synchronization control of BAM memristive neural networks with multiple proportional delays and stochastic perturbations

    Science.gov (United States)

    Wang, Weiping; Yuan, Manman; Luo, Xiong; Liu, Linlin; Zhang, Yao

    2018-01-01

    Proportional delay is a class of unbounded time-varying delay. A class of bidirectional associative memory (BAM) memristive neural networks with multiple proportional delays is concerned in this paper. First, we propose the model of BAM memristive neural networks with multiple proportional delays and stochastic perturbations. Furthermore, by choosing suitable nonlinear variable transformations, the BAM memristive neural networks with multiple proportional delays can be transformed into the BAM memristive neural networks with constant delays. Based on the drive-response system concept, differential inclusions theory and Lyapunov stability theory, some anti-synchronization criteria are obtained. Finally, the effectiveness of proposed criteria are demonstrated through numerical examples.

  17. Nonlinear Kalman Filtering in Affine Term Structure Models

    DEFF Research Database (Denmark)

    Christoffersen, Peter; Dorion, Christian; Jacobs, Kris

    When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... the potential of the unscented Kalman …filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman …filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive...

  18. Nonlinear Growth Models in M"plus" and SAS

    Science.gov (United States)

    Grimm, Kevin J.; Ram, Nilam

    2009-01-01

    Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear…

  19. Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes

    DEFF Research Database (Denmark)

    Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan

    2013-01-01

    The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...

  20. Topological approximation of the nonlinear Anderson model

    Science.gov (United States)

    Milovanov, Alexander V.; Iomin, Alexander

    2014-06-01

    We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

  1. A non-linear state space approach to model groundwater fluctuations

    NARCIS (Netherlands)

    Berendrecht, W.L.; Heemink, A.W.; Geer, F.C. van; Gehrels, J.C.

    2006-01-01

    A non-linear state space model is developed for describing groundwater fluctuations. Non-linearity is introduced by modeling the (unobserved) degree of water saturation of the root zone. The non-linear relations are based on physical concepts describing the dependence of both the actual

  2. Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

    Directory of Open Access Journals (Sweden)

    Oliveira Rui

    2010-09-01

    Full Text Available Abstract Background This paper presents a method for modelling dynamical biochemical networks with intrinsic time delays. Since the fundamental mechanisms leading to such delays are many times unknown, non conventional modelling approaches become necessary. Herein, a hybrid semi-parametric identification methodology is proposed in which discrete time series are incorporated into fundamental material balance models. This integration results in hybrid delay differential equations which can be applied to identify unknown cellular dynamics. Results The proposed hybrid modelling methodology was evaluated using two case studies. The first of these deals with dynamic modelling of transcriptional factor A in mammalian cells. The protein transport from the cytosol to the nucleus introduced a delay that was accounted for by discrete time series formulation. The second case study focused on a simple network with distributed time delays that demonstrated that the discrete time delay formalism has broad applicability to both discrete and distributed delay problems. Conclusions Significantly better prediction qualities of the novel hybrid model were obtained when compared to dynamical structures without time delays, being the more distinctive the more significant the underlying system delay is. The identification of the system delays by studies of different discrete modelling delays was enabled by the proposed structure. Further, it was shown that the hybrid discrete delay methodology is not limited to discrete delay systems. The proposed method is a powerful tool to identify time delays in ill-defined biochemical networks.

  3. Augmented twin-nonlinear two-box behavioral models for multicarrier LTE power amplifiers.

    Science.gov (United States)

    Hammi, Oualid

    2014-01-01

    A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.

  4. Parametric Identification of Nonlinear Dynamical Systems

    Science.gov (United States)

    Feeny, Brian

    2002-01-01

    In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

  5. A new car-following model with two delays

    International Nuclear Information System (INIS)

    Yu, Lei; Shi, Zhong-ke; Li, Tong

    2014-01-01

    A new car-following model is proposed by taking into account two different time delays in sensing headway and velocity. The effect of time delays on the stability analysis is studied. The theoretical and numerical results show that traffic jams are suppressed efficiently when the difference between two time delays decreases and those can be described by the solution of the modified Korteweg–de Vries (mKdV) equation. Traffic flow is more stable with two delays in headway and velocity than in the case with only one delay in headway. The impact of local small disturbance to the system is also studied.

  6. A nonlinear model for AC induced corrosion

    Directory of Open Access Journals (Sweden)

    N. Ida

    2012-09-01

    Full Text Available The modeling of corrosion poses particular difficulties. The understanding of corrosion as an electrochemical process has led to simple capacitive-resistive models that take into account the resistance of the electrolytic cell and the capacitive effect of the surface potential at the interface between conductors and the electrolyte. In some models nonlinear conduction effects have been added to account for more complex observed behavior. While these models are sufficient to describe the behavior in systems with cathodic protection, the behavior in the presence of induced AC currents from power lines and from RF sources cannot be accounted for and are insufficient to describe the effects observed in the field. Field observations have shown that a rectifying effect exists that affects the cathodic protection potential and this effect is responsible for corrosion in the presence of AC currents. The rectifying effects of the metal-corrosion interface are totally missing from current models. This work proposes a nonlinear model based on finite element analysis that takes into account the nonlinear behavior of the metal-oxide interface and promises to improve modeling by including the rectification effects at the interface.

  7. Coherence resonance in an excitable system with time delay

    International Nuclear Information System (INIS)

    Sethia, Gautam C.; Kurths, Juergen; Sen, Abhijit

    2007-01-01

    We study the noise activated dynamics of a model excitable system that consists of a subcritical Hopf oscillator with a time delayed nonlinear feedback. The coherence of the noise driven pulses of the system exhibits a novel double peaked structure as a function of the noise amplitude. The two peaks correspond to separate optimal noise levels for excitation of single spikes and multiple spikes (bursts) respectively. The relative magnitudes of these peaks are found to be a sensitive function of time delay. The physical significance of our results and its practical implications in various real life systems are discussed

  8. A note on chaotic synchronization of time-delay secure communication systems

    International Nuclear Information System (INIS)

    Li Demin; Wang Zidong; Zhou Jie; Fang Jianan; Ni Jinjin

    2008-01-01

    In a real world, the signals are often transmitted through a hostile environment, and therefore the secure communication system has attracted considerable research interests. In this paper, the observer-based chaotic synchronization problem is studied for a class of time-delay secure communication systems. The system under consideration is subject to delayed state and nonlinear disturbances. The time-delay is allowed to be time-varying, and the nonlinearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of a synchronization scheme such that, for the admissible time-delay as well as nonlinear disturbances, the response system can globally synchronize the driving system. An effective algebraic matrix inequality approach is developed to solve the chaotic synchronization problem. A numerical example is presented to show the effectiveness and efficiency of the proposed secure communication scheme

  9. Regenerative memory in time-delayed neuromorphic photonic resonators

    Science.gov (United States)

    Romeira, B.; Avó, R.; Figueiredo, José M. L.; Barland, S.; Javaloyes, J.

    2016-01-01

    We investigate a photonic regenerative memory based upon a neuromorphic oscillator with a delayed self-feedback (autaptic) connection. We disclose the existence of a unique temporal response characteristic of localized structures enabling an ideal support for bits in an optical buffer memory for storage and reshaping of data information. We link our experimental implementation, based upon a nanoscale nonlinear resonant tunneling diode driving a laser, to the paradigm of neuronal activity, the FitzHugh-Nagumo model with delayed feedback. This proof-of-concept photonic regenerative memory might constitute a building block for a new class of neuron-inspired photonic memories that can handle high bit-rate optical signals.

  10. Comparison of a nonlinear dynamic model of a piping system to test data

    International Nuclear Information System (INIS)

    Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.

    1983-01-01

    Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)

  11. Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

    Science.gov (United States)

    Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

    2017-11-01

    We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

  12. Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

    Science.gov (United States)

    Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

    2017-11-01

    We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

  13. International Conference on Structural Nonlinear Dynamics and Diagnosis

    CERN Document Server

    CSNDD 2012; CSNDD 2014

    2015-01-01

    This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics.  Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characteriz...

  14. New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

    Science.gov (United States)

    Chen, Yonggang; Bi, Weiping; Li, Wenlin

    2011-07-01

    In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.

  15. Background field method for nonlinear σ-model in stochastic quantization

    International Nuclear Information System (INIS)

    Nakazawa, Naohito; Ennyu, Daiji

    1988-01-01

    We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model. (orig.)

  16. Performance Improvement of Sensorless Vector Control for Induction Motor Drives Fed by Matrix Converter Using Nonlinear Model and Disturbance Observer

    DEFF Research Database (Denmark)

    Lee, Kyo-Beum; Blaabjerg, Frede

    2004-01-01

    This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with a non-linearity compensation and disturbance observer. The nonlinear voltage distortion that is caused by communication delay and on-state voltage drop in switching...

  17. Modeling Non-Linear Material Properties in Composite Materials

    Science.gov (United States)

    2016-06-28

    Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions

  18. Dynamics of a delayed intraguild predation model with harvesting

    Science.gov (United States)

    Collera, Juancho A.; Balilo, Aldrin T.

    2018-03-01

    In [1], a delayed three-species intraguild predation (IGP) model was considered. This particular tri-trophic community module includes a predator and its prey which share a common basal resource for their sustenance [3]. Here, it is assumed that in the absence of predation, the growth of the basal resource follows the delayed logistic equation. Without delay time, the IGP model in [1] reduces to the system considered in [7] where it was shown that IGP may induce chaos even if the functional responses are linear. Meanwhile, in [2] the delayed IGP model in [1] was generalized to include harvesting. Under the assumption that the basal resource has some economic value, a constant harvesting term on the basal resource was incorporated. However, both models in [1] and [2] use the delay time as the main parameter. In this research, we studied the delayed IGP model in [1] with the addition of linear harvesting term on each of the three species. The dynamical behavior of this system is examined using the harvesting rates as main parameter. In particular, we give conditions on the existence, stability, and bifurcations of equilibrium solutions of this system. This allows us to better understand the effects of harvesting in terms of the survival or extinction of one or more species in our system. Numerical simulations are carried out to illustrate our results. In fact, we show that the chaotic behavior in [7] unfolds when the harvesting rate parameter is varied.

  19. Third order differential equations with delay

    Directory of Open Access Journals (Sweden)

    Petr Liška

    2015-05-01

    Full Text Available In this paper, we study the oscillation and asymptotic properties of solutions of certain nonlinear third order differential equations with delay. In particular, we extend results of I. Mojsej (Nonlinear Analysis 68, 2008 and we improve conditions on the property B of N. Parhi and S. Padhi (Indian J. Pure Appl. Math., 33, 2002.

  20. Improved Delay-Dependent Robust Stability Criteria for a Class of Uncertain Neutral Type Lur’e Systems with Discrete and Distributed Delays

    Directory of Open Access Journals (Sweden)

    Kaibo Shi

    2014-01-01

    Full Text Available This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.

  1. A deep belief network with PLSR for nonlinear system modeling.

    Science.gov (United States)

    Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

    2017-10-31

    Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

  2. Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process

    Directory of Open Access Journals (Sweden)

    Dazi Li

    2015-01-01

    Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.

  3. Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials

    International Nuclear Information System (INIS)

    Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan

    2007-01-01

    A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models

  4. Robust nonlinear control design with application to a marine cooling system

    DEFF Research Database (Denmark)

    Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon

    2012-01-01

    . In this context, we apply a bilinear transformation to obtain a well-posed H-inf problem. The design procedure is applied to a marine cooling system with flow dependent delays and performance of the resulting control design is evaluated through a simulation example where a comparison is made to a linear control......In this paper we consider design of control laws for a class of nonlinear systems with time-varying state delays by use of principles from feedback linearization. To deal with model uncertainties and delay mismatches, a robust linear H-inf controller is designed for the feedback linearized system...

  5. Preisach hysteresis model for non-linear 2D heat diffusion

    International Nuclear Information System (INIS)

    Jancskar, Ildiko; Ivanyi, Amalia

    2006-01-01

    This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way

  6. Robust model predictive control for constrained continuous-time nonlinear systems

    Science.gov (United States)

    Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

    2018-02-01

    In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

  7. Modelling female fertility traits in beef cattle using linear and non-linear models.

    Science.gov (United States)

    Naya, H; Peñagaricano, F; Urioste, J I

    2017-06-01

    Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2  linear models; h 2  > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.

  8. Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

    Directory of Open Access Journals (Sweden)

    Nicolás Peréz Alvarez

    2015-11-01

    Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

  9. Experimental verification of the intrinsic ultrafast delayed nonlinearity of gold

    DEFF Research Database (Denmark)

    Bache, Morten; Lysenko, Oleg; Olivier, Nicolas

    2017-01-01

    Surface plasmon polaritons (SPPs) in plasmonic metal waveguides can excite a third-order nonlinear response [1] much akin the well-known self-phase modulation (SPM) and two-photon absorption seen in light propagating in dielectric waveguides. In metals, the nonlinearity mainly arises as a self...

  10. Phase models and clustering in networks of oscillators with delayed coupling

    Science.gov (United States)

    Campbell, Sue Ann; Wang, Zhen

    2018-01-01

    We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.

  11. Perturbation analysis of nonlinear matrix population models

    Directory of Open Access Journals (Sweden)

    Hal Caswell

    2008-03-01

    Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

  12. Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

    Science.gov (United States)

    Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

    2016-10-31

    Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

  13. Delay-Dependent Asymptotic Stability of Cohen-Grossberg Models with Multiple Time-Varying Delays

    Directory of Open Access Journals (Sweden)

    Xiaofeng Liao

    2007-01-01

    Full Text Available Dynamical behavior of a class of Cohen-Grossberg models with multiple time-varying delays is studied in detail. Sufficient delay-dependent criteria to ensure local and global asymptotic stabilities of the equilibrium of this network are derived by constructing suitable Lyapunov functionals. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.

  14. Dissipative quantum dynamics and nonlinear sigma-model

    International Nuclear Information System (INIS)

    Tarasov, V.E.

    1992-01-01

    Sedov variational principle which is the generalization of the least action principle for the dissipative and irreversible processes and the classical dissipative mechanics in the phase space is considered. Quantum dynamics for the dissipative and irreversible processes is constructed. As an example of the dissipative quantum theory the nonlinear two-dimensional sigma-model is considered. The conformal anomaly of the energy momentum tensor trace for closed bosonic string on the affine-metric manifold is investigated. The two-loop metric beta-function for nonlinear dissipative sigma-model was calculated. The results are compared with the ultraviolet two-loop conterterms for affine-metric sigma model. 71 refs

  15. Variational Boussinesq model for strongly nonlinear dispersive waves

    NARCIS (Netherlands)

    Lawrence, C.; Adytia, D.; van Groesen, E.

    2018-01-01

    For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be

  16. Nonlinear Inertia Classification Model and Application

    Directory of Open Access Journals (Sweden)

    Mei Wang

    2014-01-01

    Full Text Available Classification model of support vector machine (SVM overcomes the problem of a big number of samples. But the kernel parameter and the punishment factor have great influence on the quality of SVM model. Particle swarm optimization (PSO is an evolutionary search algorithm based on the swarm intelligence, which is suitable for parameter optimization. Accordingly, a nonlinear inertia convergence classification model (NICCM is proposed after the nonlinear inertia convergence (NICPSO is developed in this paper. The velocity of NICPSO is firstly defined as the weighted velocity of the inertia PSO, and the inertia factor is selected to be a nonlinear function. NICPSO is used to optimize the kernel parameter and a punishment factor of SVM. Then, NICCM classifier is trained by using the optical punishment factor and the optical kernel parameter that comes from the optimal particle. Finally, NICCM is applied to the classification of the normal state and fault states of online power cable. It is experimentally proved that the iteration number for the proposed NICPSO to reach the optimal position decreases from 15 to 5 compared with PSO; the training duration is decreased by 0.0052 s and the recognition precision is increased by 4.12% compared with SVM.

  17. Comparison of three nonlinear filters for fault detection in continuous glucose monitors.

    Science.gov (United States)

    Mahmoudi, Zeinab; Wendt, Sabrina Lyngbye; Boiroux, Dimitri; Hagdrup, Morten; Norgaard, Kirsten; Poulsen, Niels Kjolstad; Madsen, Henrik; Jorgensen, John Bagterp

    2016-08-01

    The purpose of this study is to compare the performance of three nonlinear filters in online drift detection of continuous glucose monitors. The nonlinear filters are the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the particle filter (PF). They are all based on a nonlinear model of the glucose-insulin dynamics in people with type 1 diabetes. Drift is modelled by a Gaussian random walk and is detected based on the statistical tests of the 90-min prediction residuals of the filters. The unscented Kalman filter had the highest average F score of 85.9%, and the smallest average detection delay of 84.1%, with the average detection sensitivity of 82.6%, and average specificity of 91.0%.

  18. Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

    DEFF Research Database (Denmark)

    Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav

    model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...

  19. Nonlinear Modeling of the PEMFC Based On NNARX Approach

    OpenAIRE

    Shan-Jen Cheng; Te-Jen Chang; Kuang-Hsiung Tan; Shou-Ling Kuo

    2015-01-01

    Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accurac...

  20. A finite element model for nonlinear shells of revolution

    International Nuclear Information System (INIS)

    Cook, W.A.

    1979-01-01

    A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)

  1. Heeding the waveform inversion nonlinearity by unwrapping the model and data

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-01-01

    Unlike traveltime inversion, waveform inversion provides relatively higher-resolution inverted models. This feature, however, comes at the cost of introducing complex nonlinearity to the inversion operator complicating the convergence process. We use unwrapped-phase-based objective functions to reduce such nonlinearity in a domain in which the high-frequency component is given by the traveltime inversion. Such information is packaged in a frequency-dependent attribute (or traveltime) that can be easily manipulated at different frequencies. It unwraps the phase of the wavefield yielding far less nonlinearity in the objective function than those experienced with the conventional misfit objective function, and yet it still holds most of the critical waveform information in its frequency dependency. However, it suffers from nonlinearity introduced by the model (or reflectivity), as events interact with each other (something like cross talk). This stems from the sinusoidal nature of the band-limited reflectivity model. Unwrapping the phase for such a model can mitigate this nonlinearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced nonlinearity and, thus, make the inversion more convergent. Simple examples are used to highlight such features.

  2. Estimation of Nonlinear DC-Motor Models Using a Sensitivity Approach

    DEFF Research Database (Denmark)

    Knudsen, Morten; Jensen, J.G.

    1995-01-01

    A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed.......A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed....

  3. Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach

    NARCIS (Netherlands)

    Doeswijk, T.G.; Keesman, K.J.

    2005-01-01

    Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such

  4. Comments on Nonlinear Sigma Models Coupled to Supergravity arXiv

    CERN Document Server

    Ferrara, Sergio

    2017-12-10

    N=1 , D=4 nonlinear sigma models, parametrized by chiral superfields, usually describe Kählerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kähler when local supersymmetry becomes nonlinearly realized through the nilpotency of the supergravity auxiliary fields. In some cases the nonlinear realization eliminates one scalar propagating degree of freedom. This happens when the sigma model conformal-frame metric has co-rank 2. In the geometry of the inflaton, this effect eliminates its scalar superpartner. We show that the sigma model metric remains semidefinite positive in all cases, due the to positivity properties of the conformal-frame sigma model metric.

  5. Nonlinear Model Predictive Control for Solid Oxide Fuel Cell System Based On Wiener Model

    OpenAIRE

    T. H. Lee; J. H. Park; S. M. Lee; S. C. Lee

    2010-01-01

    In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of ...

  6. The dynamics of second-order equations with delayed feedback and a large coefficient of delayed control

    Science.gov (United States)

    Kashchenko, Sergey A.

    2016-12-01

    The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.

  7. Lukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models

    CERN Document Server

    Baianu, I C

    2004-01-01

    A categorical and Lukasiewicz-Topos framework for Lukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Lukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Lukasiewicz Topos with an n-valued Lukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.

  8. Predictable nonlinear dynamics: Advances and limitations

    International Nuclear Information System (INIS)

    Anosov, L.A.; Butkovskii, O.Y.; Kravtsov, Y.A.; Surovyatkina, E.D.

    1996-01-01

    Methods for reconstruction chaotic dynamical system structure directly from experimental time series are described. Effectiveness of general methods is illustrated with the results of numerical simulation. It is of common interest that from the single time series it is possible to reconstruct a set of interconnected variables. Predictive power of dynamical models, provided by the nonlinear dynamics inverse problem solution, is limited firstly by the noise level in the system under study and is characterized by the horizon of predictability. New physical results are presented, concerning nonstationary and bifurcation nonlinear systems: (1) algorithms for revealing of nonstationarity in random-like chaotic time-series are suggested based on discriminant analysis with nonlinear discriminant function; (2) an opportunity is established to predict the final state in bifurcation system with quickly varying control parameters; (3) hysteresis is founded out in bifurcation system with quickly varying parameters; (4) delayed correlation left-angle noise-prediction error right-angle in chaotic systems is revealed. copyright 1996 American Institute of Physics

  9. An approach to normal forms of Kuramoto model with distributed delays and the effect of minimal delay

    Energy Technology Data Exchange (ETDEWEB)

    Niu, Ben, E-mail: niubenhit@163.com [Department of Mathematics, Harbin Institute of Technology, Weihai 264209 (China); Guo, Yuxiao [Department of Mathematics, Harbin Institute of Technology, Weihai 264209 (China); Jiang, Weihua [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China)

    2015-09-25

    Heterogeneous delays with positive lower bound (gap) are taken into consideration in Kuramoto model. On the Ott–Antonsen's manifold, the dynamical transitional behavior from incoherence to coherence is mediated by Hopf bifurcation. We establish a perturbation technique on complex domain, by which universal normal forms, stability and criticality of the Hopf bifurcation are obtained. Theoretically, a hysteresis loop is found near the subcritically bifurcated coherent state. With respect to Gamma distributed delay with fixed mean and variance, we find that the large gap decreases Hopf bifurcation value, induces supercritical bifurcations, avoids the hysteresis loop and significantly increases in the number of coexisting coherent states. The effect of gap is finally interpreted from the viewpoint of excess kurtosis of Gamma distribution. - Highlights: • Heterogeneously delay-coupled Kuramoto model with minimal delay is considered. • Perturbation technique on complex domain is established for bifurcation analysis. • Hysteresis phenomenon is investigated in a theoretical way. • The effect of excess kurtosis of distributed delays is discussed.

  10. Nonlinear control of the Salnikov model reaction

    DEFF Research Database (Denmark)

    Recke, Bodil; Jørgensen, Sten Bay

    1999-01-01

    This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...

  11. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    Haiyan Yuan

    2013-01-01

    Full Text Available This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of (k,l-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a (k,l-algebraically stable two-step Runge-Kutta method with 0

  12. Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity

    Directory of Open Access Journals (Sweden)

    Isao Ishida

    2015-01-01

    Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.

  13. Linear and non-linear amplification of high-mode perturbations at the ablation front in HiPER targets

    Energy Technology Data Exchange (ETDEWEB)

    Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)

    2011-01-15

    The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

  14. Modelling Loudspeaker Non-Linearities

    DEFF Research Database (Denmark)

    Agerkvist, Finn T.

    2007-01-01

    This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...

  15. Nonlinear Modelling of Low Frequency Loudspeakers

    DEFF Research Database (Denmark)

    Olsen, Erling Sandermann

    1997-01-01

    In the Danish LoDist project on distortion from dynamic low frequency loudspeakers a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...

  16. Nonlinear Modelling of Low Frequency Loudspeakers

    DEFF Research Database (Denmark)

    Olsen, Erling Sandermann

    1997-01-01

    In the Danish LoDist project on distortion from dynamic low-frequency loudspeakers, a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...

  17. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  18. A simple numerical model of a geometrically nonlinear Timoshenko beam

    NARCIS (Netherlands)

    Keijdener, C.; Metrikine, A.

    2015-01-01

    In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and

  19. Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

    Science.gov (United States)

    Nguyen, Nhan; Ting, Eric

    2018-01-01

    This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

  20. Neuromechanical tuning of nonlinear postural control dynamics

    Science.gov (United States)

    Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.

    2009-06-01

    Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

  1. Modeling and non-linear responses of MEMS capacitive accelerometer

    Directory of Open Access Journals (Sweden)

    Sri Harsha C.

    2014-01-01

    Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.

  2. Probabilistic delay differential equation modeling of event-related potentials.

    Science.gov (United States)

    Ostwald, Dirk; Starke, Ludger

    2016-08-01

    "Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach. Copyright © 2016 Elsevier Inc. All rights reserved.

  3. Incorporating time-delays in S-System model for reverse engineering genetic networks.

    Science.gov (United States)

    Chowdhury, Ahsan Raja; Chetty, Madhu; Vinh, Nguyen Xuan

    2013-06-18

    In any gene regulatory network (GRN), the complex interactions occurring amongst transcription factors and target genes can be either instantaneous or time-delayed. However, many existing modeling approaches currently applied for inferring GRNs are unable to represent both these interactions simultaneously. As a result, all these approaches cannot detect important interactions of the other type. S-System model, a differential equation based approach which has been increasingly applied for modeling GRNs, also suffers from this limitation. In fact, all S-System based existing modeling approaches have been designed to capture only instantaneous interactions, and are unable to infer time-delayed interactions. In this paper, we propose a novel Time-Delayed S-System (TDSS) model which uses a set of delay differential equations to represent the system dynamics. The ability to incorporate time-delay parameters in the proposed S-System model enables simultaneous modeling of both instantaneous and time-delayed interactions. Furthermore, the delay parameters are not limited to just positive integer values (corresponding to time stamps in the data), but can also take fractional values. Moreover, we also propose a new criterion for model evaluation exploiting the sparse and scale-free nature of GRNs to effectively narrow down the search space, which not only reduces the computation time significantly but also improves model accuracy. The evaluation criterion systematically adapts the max-min in-degrees and also systematically balances the effect of network accuracy and complexity during optimization. The four well-known performance measures applied to the experimental studies on synthetic networks with various time-delayed regulations clearly demonstrate that the proposed method can capture both instantaneous and delayed interactions correctly with high precision. The experiments carried out on two well-known real-life networks, namely IRMA and SOS DNA repair network in

  4. Simplified Model of Nonlinear Landau Damping

    International Nuclear Information System (INIS)

    Yampolsky, N.A.; Fisch, N.J.

    2009-01-01

    The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.

  5. Bifurcation analysis of a delayed mathematical model for tumor growth

    International Nuclear Information System (INIS)

    Khajanchi, Subhas

    2015-01-01

    In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings

  6. Modelization of highly nonlinear waves in coastal regions

    Science.gov (United States)

    Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

    2015-04-01

    The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.

  7. On control of Hopf bifurcation in time-delayed neural network system

    International Nuclear Information System (INIS)

    Zhou Shangbo; Liao Xiaofeng; Yu Juebang; Wong Kwokwo

    2005-01-01

    The control of Hopf bifurcations in neural network systems is studied in this Letter. The asymptotic stability theorem and the relevant corollary for linearized nonlinear dynamical systems are proven. In particular, a novel method for analyzing the local stability of a dynamical system with time-delay is suggested. For the time-delayed system consisting of one or two neurons, a washout filter based control model is proposed and analyzed. By employing the stability theorems derived, we investigate the stability of a control system and state the relevant theorems for choosing the parameters of the stabilized control system

  8. Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction

    International Nuclear Information System (INIS)

    Upadrashta, Deepesh; Yang, Yaowen

    2015-01-01

    Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction. (paper)

  9. Four-channel delay generator model 5740

    International Nuclear Information System (INIS)

    Baumatz, D.; Milner, M.

    1978-01-01

    The 4-channel delay generator model 5740 generates 4-pulse groups in independent channels. The device offers the possibility of controlling both the time intervals between the pulses of a group and the rate of generation of groups

  10. Charging-delay effect on longitudinal dust acoustic shock wave in strongly coupled dusty plasma

    International Nuclear Information System (INIS)

    Ghosh, Samiran; Gupta, M.R.

    2005-01-01

    Taking into account the charging-delay effect, the nonlinear propagation characteristics of longitudinal dust acoustic wave in strongly coupled collisional dusty plasma described by generalized hydrodynamic model have been investigated. In the 'hydrodynamic limit', a Korteweg-de Vries Burger (KdVB) equation with a damping term arising due to dust-neutral collision is derived in which the Burger term is proportional to the dissipation due to dust viscosity through dust-dust correlation and charging-delay-induced anomalous dissipation. On the other hand, in the 'kinetic limit', a KdVB equation with a damping term and a nonlocal nonlinear forcing term arising due to memory-dependent strong correlation effect of dust fluid is derived in which the Burger term depends only on the charging-delay-induced dissipation. Numerical solution of integrodifferential equations reveals that (i) dissipation due to dust viscosity and principally due to charging delay causes excitation of the longitudinal dust acoustic shock wave in strongly coupled dusty plasma and (ii) dust-neutral collision does not appear to play any direct role in shock formation. The condition for the generation of shock is also discussed briefly

  11. A Data-Driven Air Transportation Delay Propagation Model Using Epidemic Process Models

    Directory of Open Access Journals (Sweden)

    B. Baspinar

    2016-01-01

    Full Text Available In air transport network management, in addition to defining the performance behavior of the system’s components, identification of their interaction dynamics is a delicate issue in both strategic and tactical decision-making process so as to decide which elements of the system are “controlled” and how. This paper introduces a novel delay propagation model utilizing epidemic spreading process, which enables the definition of novel performance indicators and interaction rates of the elements of the air transportation network. In order to understand the behavior of the delay propagation over the network at different levels, we have constructed two different data-driven epidemic models approximating the dynamics of the system: (a flight-based epidemic model and (b airport-based epidemic model. The flight-based epidemic model utilizing SIS epidemic model focuses on the individual flights where each flight can be in susceptible or infected states. The airport-centric epidemic model, in addition to the flight-to-flight interactions, allows us to define the collective behavior of the airports, which are modeled as metapopulations. In network model construction, we have utilized historical flight-track data of Europe and performed analysis for certain days involving certain disturbances. Through this effort, we have validated the proposed delay propagation models under disruptive events.

  12. Nonlinear Prediction Model for Hydrologic Time Series Based on Wavelet Decomposition

    Science.gov (United States)

    Kwon, H.; Khalil, A.; Brown, C.; Lall, U.; Ahn, H.; Moon, Y.

    2005-12-01

    Traditionally forecasting and characterizations of hydrologic systems is performed utilizing many techniques. Stochastic linear methods such as AR and ARIMA and nonlinear ones such as statistical learning theory based tools have been extensively used. The common difficulty to all methods is the determination of sufficient and necessary information and predictors for a successful prediction. Relationships between hydrologic variables are often highly nonlinear and interrelated across the temporal scale. A new hybrid approach is proposed for the simulation of hydrologic time series combining both the wavelet transform and the nonlinear model. The present model employs some merits of wavelet transform and nonlinear time series model. The Wavelet Transform is adopted to decompose a hydrologic nonlinear process into a set of mono-component signals, which are simulated by nonlinear model. The hybrid methodology is formulated in a manner to improve the accuracy of a long term forecasting. The proposed hybrid model yields much better results in terms of capturing and reproducing the time-frequency properties of the system at hand. Prediction results are promising when compared to traditional univariate time series models. An application of the plausibility of the proposed methodology is provided and the results conclude that wavelet based time series model can be utilized for simulating and forecasting of hydrologic variable reasonably well. This will ultimately serve the purpose of integrated water resources planning and management.

  13. Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

    Directory of Open Access Journals (Sweden)

    Xinze Lian

    2013-01-01

    Full Text Available We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.

  14. Mixed Modeling of a SAW Delay Line Using VHDL-AMS

    Science.gov (United States)

    Wilson, William C.; Atkinson, Gary M.

    2006-01-01

    To aid in the development of SAW sensors for aerospace applications we have created a model of a SAW Delay line using VHDL. The model implements the Impulse Response method to calculate the frequency response, impedance, and insertion loss. The model includes optimization for the number of finger pairs in the IDTs and for the aperture height. This paper presents the model and the results from the model for a SAW delay line design.

  15. Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval

    Science.gov (United States)

    Shi, Xiangyun; Kuang, Yang; Makroglou, Athena; Mokshagundam, Sriprakash; Li, Jiaxu

    2017-11-01

    Type 2 diabetes mellitus (T2DM) has become prevalent pandemic disease in view of the modern life style. Both diabetic population and health expenses grow rapidly according to American Diabetes Association. Detecting the potential onset of T2DM is an essential focal point in the research of diabetes mellitus. The intravenous glucose tolerance test (IVGTT) is an effective protocol to determine the insulin sensitivity, glucose effectiveness, and pancreatic β-cell functionality, through the analysis and parameter estimation of a proper differential equation model. Delay differential equations have been used to study the complex physiological phenomena including the glucose and insulin regulations. In this paper, we propose a novel approach to model the time delay in IVGTT modeling. This novel approach uses two parameters to simulate not only both discrete time delay and distributed time delay in the past interval, but also the time delay distributed in a past sub-interval. Normally, larger time delay, either a discrete or a distributed delay, will destabilize the system. However, we find that time delay over a sub-interval might not. We present analytically some basic model properties, which are desirable biologically and mathematically. We show that this relatively simple model provides good fit to fluctuating patient data sets and reveals some intriguing dynamics. Moreover, our numerical simulation results indicate that our model may remove the defect in well known Minimal Model, which often overestimates the glucose effectiveness index.

  16. Robust nonlinear control of nuclear reactors under model uncertainty

    International Nuclear Information System (INIS)

    Park, Moon Ghu

    1993-02-01

    A nonlinear model-based control method is developed for the robust control of a nuclear reactor. The nonlinear plant model is used to design a unique control law which covers a wide operating range. The robustness is a crucial factor for the fully automatic control of reactor power due to time-varying, uncertain parameters, and state estimation error, or unmodeled dynamics. A variable structure control (VSC) method is introduced which consists of an adaptive performance specification (fime control) after the tracking error reaches the narrow boundary-layer by a time-optimal control (coarse control). Variable structure control is a powerful method for nonlinear system controller design which has inherent robustness to parameter variations or external disturbances using the known uncertainty bounds, and it requires very low computational efforts. In spite of its desirable properties, conventional VSC presents several important drawbacks that limit its practical applicability. One of the most undesirable phenomena is chattering, which implies extremely high control activity and may excite high-frequency unmodeled dynamics. This problem is due to the neglected actuator time-delay or sampling effects. The problem was partially remedied by replacing chattering control by a smooth control inter-polation in a boundary layer neighnboring a time-varying sliding surface. But, for the nuclear reactor systems which has very fast dynamic response, the sampling effect may destroy the narrow boundary layer when a large uncertainty bound is used. Due to the very short neutron life time, large uncertainty bound leads to the high gain in feedback control. To resolve this problem, a derivative feedback is introduced that gives excellent performance by reducing the uncertainty bound. The stability of tracking error dynamics is guaranteed by the second method of Lyapunov using the two-level uncertainty bounds that are obtained from the knowledge of uncertainty bound and the estimated

  17. Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell–Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model

    International Nuclear Information System (INIS)

    Lorin, E; Bandrauk, A D; Lytova, M; Memarian, A

    2015-01-01

    This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser–molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [1, 2], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [3–9]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects. (paper)

  18. Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

    Science.gov (United States)

    Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

    2018-04-01

    We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

  19. Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter

    Science.gov (United States)

    Wang, Ye; Ramirez-Jaime, Andres; Xu, Feng; Puig, Vicenç

    2017-01-01

    This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and position are nonlinear, which are quite sensitive to changes of inputs and disturbances. By means of constraint satisfactions, partial nonlinearities and modeling errors of the control-oriented model of full dynamics can be transformed into the inequality constraints. Subsequently, the quadcopter can be controlled by an NMPC controller with the updated constraints generated by constraint satisfactions. Finally, the simulation results applied to a quadcopter simulator are provided to show the effectiveness of the proposed strategy.

  20. Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

    DEFF Research Database (Denmark)

    Bache, Morten; Lavrinenko, Andrei

    2017-01-01

    Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still...

  1. Modelling the Probability Density Function of IPTV Traffic Packet Delay Variation

    Directory of Open Access Journals (Sweden)

    Michal Halas

    2012-01-01

    Full Text Available This article deals with modelling the Probability density function of IPTV traffic packet delay variation. The use of this modelling is in an efficient de-jitter buffer estimation. When an IP packet travels across a network, it experiences delay and its variation. This variation is caused by routing, queueing systems and other influences like the processing delay of the network nodes. When we try to separate these at least three types of delay variation, we need a way to measure these types separately. This work is aimed to the delay variation caused by queueing systems which has the main implications to the form of the Probability density function.

  2. A simple chaotic delay differential equation

    International Nuclear Information System (INIS)

    Sprott, J.C.

    2007-01-01

    The simplest chaotic delay differential equation with a sinusoidal nonlinearity is described, including the route to chaos, Lyapunov exponent spectrum, and chaotic diffusion. It is prototypical of many other high-dimensional chaotic systems

  3. Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant

    Directory of Open Access Journals (Sweden)

    Xiangjie Liu

    2014-01-01

    Full Text Available Reliable power and temperature control in pressurized water reactor (PWR nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC, by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.

  4. COMBINING LONG MEMORY AND NONLINEAR MODEL OUTPUTS FOR INFLATION FORECAST

    OpenAIRE

    Heri Kuswanto; Irhamah Alimuhajin; Laylia Afidah

    2014-01-01

    Long memory and nonlinearity have been proven as two models that are easily to be mistaken. In other words, nonlinearity is a strong candidate of spurious long memory by introducing a certain degree of fractional integration that lies in the region of long memory. Indeed, nonlinear process belongs to short memory with zero integration order. The idea of the forecast is to obtain the future condition with minimum error. Some researches argued that no matter what the model is, the important thi...

  5. Evaluation of performance of distributed delay model for chemotherapy-induced myelosuppression.

    Science.gov (United States)

    Krzyzanski, Wojciech; Hu, Shuhua; Dunlavey, Michael

    2018-04-01

    The distributed delay model has been introduced that replaces the transit compartments in the classic model of chemotherapy-induced myelosuppression with a convolution integral. The maturation of granulocyte precursors in the bone marrow is described by the gamma probability density function with the shape parameter (ν). If ν is a positive integer, the distributed delay model coincides with the classic model with ν transit compartments. The purpose of this work was to evaluate performance of the distributed delay model with particular focus on model deterministic identifiability in the presence of the shape parameter. The classic model served as a reference for comparison. Previously published white blood cell (WBC) count data in rats receiving bolus doses of 5-fluorouracil were fitted by both models. The negative two log-likelihood objective function (-2LL) and running times were used as major markers of performance. Local sensitivity analysis was done to evaluate the impact of ν on the pharmacodynamics response WBC. The ν estimate was 1.46 with 16.1% CV% compared to ν = 3 for the classic model. The difference of 6.78 in - 2LL between classic model and the distributed delay model implied that the latter performed significantly better than former according to the log-likelihood ratio test (P = 0.009), although the overall performance was modestly better. The running times were 1 s and 66.2 min, respectively. The long running time of the distributed delay model was attributed to computationally intensive evaluation of the convolution integral. The sensitivity analysis revealed that ν strongly influences the WBC response by controlling cell proliferation and elimination of WBCs from the circulation. In conclusion, the distributed delay model was deterministically identifiable from typical cytotoxic data. Its performance was modestly better than the classic model with significantly longer running time.

  6. Nonlinear friction model for servo press simulation

    Science.gov (United States)

    Ma, Ninshu; Sugitomo, Nobuhiko; Kyuno, Takunori; Tamura, Shintaro; Naka, Tetsuo

    2013-12-01

    The friction coefficient was measured under an idealized condition for a pulse servo motion. The measured friction coefficient and its changing with both sliding distance and a pulse motion showed that the friction resistance can be reduced due to the re-lubrication during unloading process of the pulse servo motion. Based on the measured friction coefficient and its changes with sliding distance and re-lubrication of oil, a nonlinear friction model was developed. Using the newly developed the nonlinear friction model, a deep draw simulation was performed and the formability was evaluated. The results were compared with experimental ones and the effectiveness was verified.

  7. Mathematical models for suspension bridges nonlinear structural instability

    CERN Document Server

    Gazzola, Filippo

    2015-01-01

    This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

  8. Delay induced stability switch, multitype bistability and chaos in an intraguild predation model.

    Science.gov (United States)

    Shu, Hongying; Hu, Xi; Wang, Lin; Watmough, James

    2015-12-01

    In many predator-prey models, delay has a destabilizing effect and induces oscillations; while in many competition models, delay does not induce oscillations. By analyzing a rather simple delayed intraguild predation model, which combines both the predator-prey relation and competition, we show that delay in intraguild predation models promotes very complex dynamics. The delay can induce stability switches exhibiting a destabilizing role as well as a stabilizing role. It is shown that three types of bistability are possible: one stable equilibrium coexists with another stable equilibrium (node-node bistability); one stable equilibrium coexists with a stable periodic solution (node-cycle bistability); one stable periodic solution coexists with another stable periodic solution (cycle-cycle bistability). Numerical simulations suggest that delay can also induce chaos in intraguild predation models.

  9. Performance analysis of NOAA tropospheric signal delay model

    International Nuclear Information System (INIS)

    Ibrahim, Hassan E; El-Rabbany, Ahmed

    2011-01-01

    Tropospheric delay is one of the dominant global positioning system (GPS) errors, which degrades the positioning accuracy. Recent development in tropospheric modeling relies on implementation of more accurate numerical weather prediction (NWP) models. In North America one of the NWP-based tropospheric correction models is the NOAA Tropospheric Signal Delay Model (NOAATrop), which was developed by the US National Oceanic and Atmospheric Administration (NOAA). Because of its potential to improve the GPS positioning accuracy, the NOAATrop model became the focus of many researchers. In this paper, we analyzed the performance of the NOAATrop model and examined its effect on ionosphere-free-based precise point positioning (PPP) solution. We generated 3 year long tropospheric zenith total delay (ZTD) data series for the NOAATrop model, Hopfield model, and the International GNSS Services (IGS) final tropospheric correction product, respectively. These data sets were generated at ten IGS reference stations spanning Canada and the United States. We analyzed the NOAATrop ZTD data series and compared them with those of the Hopfield model. The IGS final tropospheric product was used as a reference. The analysis shows that the performance of the NOAATrop model is a function of both season (time of the year) and geographical location. However, its performance was superior to the Hopfield model in all cases. We further investigated the effect of implementing the NOAATrop model on the ionosphere-free-based PPP solution convergence and accuracy. It is shown that the use of the NOAATrop model improved the PPP solution convergence by 1%, 10% and 15% for the latitude, longitude and height components, respectively

  10. An Improved Nonlinear Five-Point Model for Photovoltaic Modules

    Directory of Open Access Journals (Sweden)

    Sakaros Bogning Dongue

    2013-01-01

    Full Text Available This paper presents an improved nonlinear five-point model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical five-point model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the five-parameter model proposed by other authors.

  11. Modelling of a bridge-shaped nonlinear piezoelectric energy harvester

    International Nuclear Information System (INIS)

    Gafforelli, G; Corigliano, A; Xu, R; Kim, S G

    2013-01-01

    Piezoelectric MicroElectroMechanical Systems (MEMS) energy harvesting is an attractive technology for harvesting small magnitudes of energy from ambient vibrations. Increasing the operating frequency bandwidth of such devices is one of the major issues for real world applications. A MEMS-scale doubly clamped nonlinear beam resonator is designed and developed to demonstrate very wide bandwidth and high power density. In this paper a first complete theoretical discussion of nonlinear resonating piezoelectric energy harvesting is provided. The sectional behaviour of the beam is studied through the Classical Lamination Theory (CLT) specifically modified to introduce the piezoelectric coupling and nonlinear Green-Lagrange strain tensor. A lumped parameter model is built through Rayleigh-Ritz Method and the resulting nonlinear coupled equations are solved in the frequency domain through the Harmonic Balance Method (HBM). Finally, the influence of external load resistance on the dynamic behaviour is studied. The theoretical model shows that nonlinear resonant harvesters have much wider power bandwidth than that of linear resonators but their maximum power is still bounded by the mechanical damping as is the case for linear resonating harvesters

  12. Bifurcations of Tumor-Immune Competition Systems with Delay

    Directory of Open Access Journals (Sweden)

    Ping Bi

    2014-01-01

    Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.

  13. Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

    International Nuclear Information System (INIS)

    Adcock, T. A. A.; Taylor, P. H.

    2016-01-01

    The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum

  14. Control-based method to identify underlying delays of a nonlinear dynamical system.

    Science.gov (United States)

    Yu, Dongchuan; Frasca, Mattia; Liu, Fang

    2008-10-01

    We suggest several stationary state control-based delay identification methods which do not require any structural information about the controlled systems and are applicable to systems described by delayed ordinary differential equations. This proposed technique includes three steps: (i) driving a system to a steady state; (ii) perturbing the control signal for shifting the steady state; and (iii) identifying all delays by detecting the time that the system is abruptly drawn out of stationarity. Some aspects especially important for applications are discussed as well, including interaction delay identification, stationary state convergence speed, performance comparison, and the influence of noise on delay identification. Several examples are presented to illustrate the reliability and robustness of all delay identification methods suggested.

  15. Noise-and delay-induced phase transitions of the dimer–monomer surface reaction model

    International Nuclear Information System (INIS)

    Zeng Chunhua; Wang Hua

    2012-01-01

    Highlights: ► We study the dimer–monomer surface reaction model. ► We show that noise induces first-order irreversible phase transition (IPT). ► Combination of noise and time-delayed feedback induce first- and second-order IPT. ► First- and second-order IPT is viewed as noise-and delay-induced phase transitions. - Abstract: The effects of noise and time-delayed feedback in the dimer–monomer (DM) surface reaction model are investigated. Applying small delay approximation, we construct a stochastic delayed differential equation and its Fokker–Planck equation to describe the state evolution of the DM reaction model. We show that the noise can only induce first-order irreversible phase transition (IPT) characteristic of the DM model, however the combination of the noise and time-delayed feedback can simultaneously induce first- and second-order IPT characteristics of the DM model. Therefore, it is shown that the well-known first- and second-order IPT characteristics of the DM model may be viewed as noise-and delay-induced phase transitions.

  16. Nonlinear system identification of smart structures under high impact loads

    International Nuclear Information System (INIS)

    Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

    2013-01-01

    The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure–MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure–MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes. (paper)

  17. Nonlinear system identification of smart structures under high impact loads

    Science.gov (United States)

    Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

    2013-05-01

    The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

  18. Travelling wave solutions for some time-delayed equations through factorizations

    International Nuclear Information System (INIS)

    Fahmy, E.S.

    2008-01-01

    In this work, we use factorization method to find explicit particular travelling wave solutions for the following important nonlinear second-order partial differential equations: The generalized time-delayed Burgers-Huxley, time-delayed convective Fishers, and the generalized time-delayed Burgers-Fisher. Using the particular solutions for these equations we find the general solutions, two-parameter solution, as special cases

  19. Spatiotemporal drought forecasting using nonlinear models

    Science.gov (United States)

    Vasiliades, Lampros; Loukas, Athanasios

    2010-05-01

    Spatiotemporal data mining is the extraction of unknown and implicit knowledge, structures, spatiotemporal relationships, or patterns not explicitly stored in spatiotemporal databases. As one of data mining techniques, forecasting is widely used to predict the unknown future based upon the patterns hidden in the current and past data. In order to achieve spatiotemporal forecasting, some mature analysis tools, e.g., time series and spatial statistics are extended to the spatial dimension and the temporal dimension, respectively. Drought forecasting plays an important role in the planning and management of natural resources and water resource systems in a river basin. Early and timelines forecasting of a drought event can help to take proactive measures and set out drought mitigation strategies to alleviate the impacts of drought. Despite the widespread application of nonlinear mathematical models, comparative studies on spatiotemporal drought forecasting using different models are still a huge task for modellers. This study uses a promising approach, the Gamma Test (GT), to select the input variables and the training data length, so that the trial and error workload could be greatly reduced. The GT enables to quickly evaluate and estimate the best mean squared error that can be achieved by a smooth model on any unseen data for a given selection of inputs, prior to model construction. The GT is applied to forecast droughts using monthly Standardized Precipitation Index (SPI) timeseries at multiple timescales in several precipitation stations at Pinios river basin in Thessaly region, Greece. Several nonlinear models have been developed efficiently, with the aid of the GT, for 1-month up to 12-month ahead forecasting. Several temporal and spatial statistical indices were considered for the performance evaluation of the models. The predicted results show reasonably good agreement with the actual data for short lead times, whereas the forecasting accuracy decreases with

  20. Nonlinear adaptive inverse control via the unified model neural network

    Science.gov (United States)

    Jeng, Jin-Tsong; Lee, Tsu-Tian

    1999-03-01

    In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

  1. Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.

    Science.gov (United States)

    Niu, Ben; Li, Lu

    2018-06-01

    This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

  2. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

    Science.gov (United States)

    Shah, A A; Xing, W W; Triantafyllidis, V

    2017-04-01

    In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

  3. Nonlinear GARCH model and 1 / f noise

    Science.gov (United States)

    Kononovicius, A.; Ruseckas, J.

    2015-06-01

    Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

  4. Model reduction of nonlinear systems subject to input disturbances

    KAUST Repository

    Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2017-01-01

    The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order

  5. Non-linear auto-regressive models for cross-frequency coupling in neural time series

    Science.gov (United States)

    Tallot, Lucille; Grabot, Laetitia; Doyère, Valérie; Grenier, Yves; Gramfort, Alexandre

    2017-01-01

    We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling. PMID:29227989

  6. Time-delay-induced phase-transition to synchrony in coupled bursting neurons

    Science.gov (United States)

    Adhikari, Bhim Mani; Prasad, Awadhesh; Dhamala, Mukeshwar

    2011-06-01

    Signal transmission time delays in a network of nonlinear oscillators are known to be responsible for a variety of interesting dynamic behaviors including phase-flip transitions leading to synchrony or out of synchrony. Here, we uncover that phase-flip transitions are general phenomena and can occur in a network of coupled bursting neurons with a variety of coupling types. The transitions are marked by nonlinear changes in both temporal and phase-space characteristics of the coupled system. We demonstrate these phase-transitions with Hindmarsh-Rose and Leech-Heart interneuron models and discuss the implications of these results in understanding collective dynamics of bursting neurons in the brain.

  7. Calibration of the nonlinear ring model at the Diamond Light Source

    Directory of Open Access Journals (Sweden)

    R. Bartolini

    2011-05-01

    Full Text Available Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration of the nonlinear model that can accurately reproduce the nonlinear beam dynamics in Diamond.

  8. Modeling vector nonlinear time series using POLYMARS

    NARCIS (Netherlands)

    de Gooijer, J.G.; Ray, B.K.

    2003-01-01

    A modified multivariate adaptive regression splines method for modeling vector nonlinear time series is investigated. The method results in models that can capture certain types of vector self-exciting threshold autoregressive behavior, as well as provide good predictions for more general vector

  9. Likelihood-Based Inference in Nonlinear Error-Correction Models

    DEFF Research Database (Denmark)

    Kristensen, Dennis; Rahbæk, Anders

    We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...

  10. An overview of the recent advances in delay-time-based maintenance modelling

    International Nuclear Information System (INIS)

    Wang, Wenbin

    2012-01-01

    Industrial plant maintenance is an area which has enormous potential to be improved. It is also an area attracted significant attention from mathematical modellers because of the random phenomenon of plant failures. This paper reviews the recent advances in delay-time-based maintenance modelling, which is one of the mathematical techniques for optimising inspection planning and related problems. The delay-time is a concept that divides a plant failure process into two stages: from new until the point of an identifiable defect, and then from this point to failure. The first stage is called the normal working stage and the second stage is called the failure delay-time stage. If the distributions of the two stages can be quantified, the relationship between the number of failures and the inspection interval can be readily established. This can then be used for optimizing the inspection interval and other related decision variables. In this review, we pay particular attention to new methodological developments and industrial applications of the delay-time-based models over the last few decades. The use of the delay-time concept and modeling techniques in other areas rather than in maintenance is also reviewed. Future research directions are also highlighted. - Highlights: ► Reviewed the recent advances in delay-time-based maintenance models and applications. ► Compared the delay-time-based models with other models. ► Focused on methodologies and applications. ► Pointed out future research directions.

  11. Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

    Directory of Open Access Journals (Sweden)

    Zhenhua Hu

    2013-01-01

    Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

  12. Application of homotopy-perturbation method to nonlinear population dynamics models

    International Nuclear Information System (INIS)

    Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.

    2007-01-01

    In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)

  13. Period doubling phenomenon in a class of time delay equations

    International Nuclear Information System (INIS)

    Oliveira, C.R. de; Malta, C.P.

    1985-01-01

    The properties of the solution of a nonlinear time delayed differential equation (infinite dimension) as function of two parameters: the time delay tau and another parameter A (nonlinearity) are investigated. After a Hopf bifurcation period doubling may occur and is characterized by Feigenbaum's delta. A strange atractor is obtained after the period doubling cascade and the largest Lyapunov exponent is calculated indicating that the attractor has low dimension. The behaviour of this Liapunov exponent as function of tau is different from its behaviour as function of A. (Author) [pt

  14. Modelling and control of a nonlinear magnetostrictive actuator system

    Science.gov (United States)

    Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.

    2018-04-01

    This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.

  15. Terrestrial Sagnac delay constraining modified gravity models

    Science.gov (United States)

    Karimov, R. Kh.; Izmailov, R. N.; Potapov, A. A.; Nandi, K. K.

    2018-04-01

    Modified gravity theories include f(R)-gravity models that are usually constrained by the cosmological evolutionary scenario. However, it has been recently shown that they can also be constrained by the signatures of accretion disk around constant Ricci curvature Kerr-f(R0) stellar sized black holes. Our aim here is to use another experimental fact, viz., the terrestrial Sagnac delay to constrain the parameters of specific f(R)-gravity prescriptions. We shall assume that a Kerr-f(R0) solution asymptotically describes Earth's weak gravity near its surface. In this spacetime, we shall study oppositely directed light beams from source/observer moving on non-geodesic and geodesic circular trajectories and calculate the time gap, when the beams re-unite. We obtain the exact time gap called Sagnac delay in both cases and expand it to show how the flat space value is corrected by the Ricci curvature, the mass and the spin of the gravitating source. Under the assumption that the magnitude of corrections are of the order of residual uncertainties in the delay measurement, we derive the allowed intervals for Ricci curvature. We conclude that the terrestrial Sagnac delay can be used to constrain the parameters of specific f(R) prescriptions. Despite using the weak field gravity near Earth's surface, it turns out that the model parameter ranges still remain the same as those obtained from the strong field accretion disk phenomenon.

  16. Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

    Science.gov (United States)

    Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

    2018-05-01

    Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

  17. Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis

    Directory of Open Access Journals (Sweden)

    Moussa Leblouba

    2016-01-01

    Full Text Available Soil-shallow foundation interaction models that are incorporated into most structural analysis programs generally lack accuracy and efficiency or neglect some aspects of foundation behavior. For instance, soil-shallow foundation systems have been observed to show both small and large loops under increasing amplitude load reversals. This paper presents a practical macroelement model for soil-shallow foundation system and its stability under simultaneous horizontal and vertical loads. The model comprises three spring elements: nonlinear horizontal, nonlinear rotational, and linear vertical springs. The proposed macroelement model was verified using experimental test results from large-scale model foundations subjected to small and large cyclic loading cases.

  18. Nonlinear modeling of a rotational MR damper via an enhanced Bouc–Wen model

    International Nuclear Information System (INIS)

    Miah, Mohammad S; Chatzi, Eleni N; Dertimanis, Vasilis K; Weber, Felix

    2015-01-01

    The coupling of magnetorheological (MR) dampers with semi-active control schemes has proven to be an effective and failsafe approach for vibration mitigation of low-damped structures. However, due to the nonlinearities inherently relating to such damping devices, the characterization of the associated nonlinear phenomena is still a challenging task. Herein, an enhanced phenomenological modeling approach is proposed for the description of a rotational-type MR damper, which comprises a modified Bouc–Wen model coupled with an appropriately selected sigmoid function. In a first step, parameter optimization is performed on the basis of individual models in an effort to approximate the experimentally observed response for varying current levels and actuator force characteristics. In a second step, based on the previously identified parameters, a generalized best-fit model is proposed by performing a regression analysis. Finally, model validation is carried out via implementation on different sets of experimental data. The proposed model indeed renders an improved representation of the actually observed nonlinear behavior of the tested rotational MR damper. (paper)

  19. An analog model for quantum lightcone fluctuations in nonlinear optics

    International Nuclear Information System (INIS)

    Ford, L.H.; De Lorenci, V.A.; Menezes, G.; Svaiter, N.F.

    2013-01-01

    We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable. - Highlights: ► Lightcone fluctuations, quantum fluctuations of the effective speed of light, are a feature of quantum gravity. ► Nonlinear dielectrics have a variable speed of light, analogous to the effects of gravity. ► Fluctuating electric fields create the effect of lightcone fluctuations in a nonlinear material. ► We propose to use squeezed light in a nonlinear material as an analog model of lightcone fluctuations. ► Variation in the speed of propagation of pulses is the observational signature of lightcone fluctuations.

  20. Special class of nonlinear damping models in flexible space structures

    Science.gov (United States)

    Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

    1991-01-01

    A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

  1. Relaxation periodic solutions of one singular perturbed system with delay

    Science.gov (United States)

    Kashchenko, A. A.

    2017-12-01

    In this paper, we consider a singularly perturbed system of two differential equations with delay, simulating two coupled oscillators with a nonlinear compactly supported feedback. We reduce studying nonlocal dynamics of initial system to studying dynamics of special finite-dimensional mappings: rough stable (unstable) cycles of these mappings correspond to exponentially orbitally stable (unstable) relaxation solutions of initial problem. We show that dynamics of initial model depends on coupling coefficient crucially. Multistability is proved.

  2. Predicting the Pullout Capacity of Small Ground Anchors Using Nonlinear Integrated Computing Techniques

    Directory of Open Access Journals (Sweden)

    Mosbeh R. Kaloop

    2017-01-01

    Full Text Available This study investigates predicting the pullout capacity of small ground anchors using nonlinear computing techniques. The input-output prediction model for the nonlinear Hammerstein-Wiener (NHW and delay inputs for the adaptive neurofuzzy inference system (DANFIS are developed and utilized to predict the pullout capacity. The results of the developed models are compared with previous studies that used artificial neural networks and least square support vector machine techniques for the same case study. The in situ data collection and statistical performances are used to evaluate the models performance. Results show that the developed models enhance the precision of predicting the pullout capacity when compared with previous studies. Also, the DANFIS model performance is proven to be better than other models used to detect the pullout capacity of ground anchors.

  3. A Non-linear Stochastic Model for an Office Building with Air Infiltration

    DEFF Research Database (Denmark)

    Thavlov, Anders; Madsen, Henrik

    2015-01-01

    This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...

  4. Nonlinear modeling and identification of a DC motor for bidirectional operation with real time experiments

    International Nuclear Information System (INIS)

    Kara, Tolgay; Eker, Ilyas

    2004-01-01

    Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed

  5. On the nonlinear modeling of ring oscillators

    KAUST Repository

    Elwakil, Ahmed S.

    2009-06-01

    We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.

  6. On the nonlinear modeling of ring oscillators

    KAUST Repository

    Elwakil, Ahmed S.; Salama, Khaled N.

    2009-01-01

    We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.

  7. Nonlinear signal processing using neural networks: Prediction and system modelling

    Energy Technology Data Exchange (ETDEWEB)

    Lapedes, A.; Farber, R.

    1987-06-01

    The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

  8. A comparison of cosmological models using time delay lenses

    Energy Technology Data Exchange (ETDEWEB)

    Wei, Jun-Jie; Wu, Xue-Feng; Melia, Fulvio, E-mail: jjwei@pmo.ac.cn, E-mail: xfwu@pmo.ac.cn, E-mail: fmelia@email.arizona.edu [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China)

    2014-06-20

    The use of time-delay gravitational lenses to examine the cosmological expansion introduces a new standard ruler with which to test theoretical models. The sample suitable for this kind of work now includes 12 lens systems, which have thus far been used solely for optimizing the parameters of ΛCDM. In this paper, we broaden the base of support for this new, important cosmic probe by using these observations to carry out a one-on-one comparison between competing models. The currently available sample indicates a likelihood of ∼70%-80% that the R {sub h} = ct universe is the correct cosmology versus ∼20%-30% for the standard model. This possibly interesting result reinforces the need to greatly expand the sample of time-delay lenses, e.g., with the successful implementation of the Dark Energy Survey, the VST ATLAS survey, and the Large Synoptic Survey Telescope. In anticipation of a greatly expanded catalog of time-delay lenses identified with these surveys, we have produced synthetic samples to estimate how large they would have to be in order to rule out either model at a ∼99.7% confidence level. We find that if the real cosmology is ΛCDM, a sample of ∼150 time-delay lenses would be sufficient to rule out R {sub h} = ct at this level of accuracy, while ∼1000 time-delay lenses would be required to rule out ΛCDM if the real universe is instead R {sub h} = ct. This difference in required sample size reflects the greater number of free parameters available to fit the data with ΛCDM.

  9. A comparison of cosmological models using time delay lenses

    International Nuclear Information System (INIS)

    Wei, Jun-Jie; Wu, Xue-Feng; Melia, Fulvio

    2014-01-01

    The use of time-delay gravitational lenses to examine the cosmological expansion introduces a new standard ruler with which to test theoretical models. The sample suitable for this kind of work now includes 12 lens systems, which have thus far been used solely for optimizing the parameters of ΛCDM. In this paper, we broaden the base of support for this new, important cosmic probe by using these observations to carry out a one-on-one comparison between competing models. The currently available sample indicates a likelihood of ∼70%-80% that the R h = ct universe is the correct cosmology versus ∼20%-30% for the standard model. This possibly interesting result reinforces the need to greatly expand the sample of time-delay lenses, e.g., with the successful implementation of the Dark Energy Survey, the VST ATLAS survey, and the Large Synoptic Survey Telescope. In anticipation of a greatly expanded catalog of time-delay lenses identified with these surveys, we have produced synthetic samples to estimate how large they would have to be in order to rule out either model at a ∼99.7% confidence level. We find that if the real cosmology is ΛCDM, a sample of ∼150 time-delay lenses would be sufficient to rule out R h = ct at this level of accuracy, while ∼1000 time-delay lenses would be required to rule out ΛCDM if the real universe is instead R h = ct. This difference in required sample size reflects the greater number of free parameters available to fit the data with ΛCDM.

  10. Projective-anticipating, projective and projective-lag synchronization of chaotic systems with time-varying delays

    International Nuclear Information System (INIS)

    Feng Cunfang; Guan Wei; Wang Yinghai

    2013-01-01

    We investigate different types of projective (projective-anticipating, projective and projective-lag) synchronization in unidirectionally nonlinearly coupled time-delayed chaotic systems with variable time delays. Based on the Krasovskii–Lyapunov approach, we find both the existence and sufficient stability conditions, using a general class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. Our method has the advantage that it requires only one nonlinearly coupled term to achieve different types of projective synchronization in time-delayed chaotic systems with variable time delays. Compared with other existing works, our result provides an easy way to achieve projective-anticipating, projective and projective-lag synchronization. Numerical simulations of the Ikeda system are given to demonstrate the validity of the proposed method. (paper)

  11. Acceleration (Deceleration Model Supporting Time Delays to Refresh Data

    Directory of Open Access Journals (Sweden)

    José Gerardo Carrillo González

    2018-04-01

    Full Text Available This paper proposes a mathematical model to regulate the acceleration (deceleration applied by self-driving vehicles in car-following situations. A virtual environment is designed to test the model in different circumstances: (1 the followers decelerate in time if the leader decelerates, considering a time delay of up to 5 s to refresh data (vehicles position coordinates required by the model, (2 with the intention of optimizing space, the vehicles are grouped in platoons, where 3 s of time delay (to update data is supported if the vehicles have a centre-to-centre spacing of 20 m and a time delay of 1 s is supported at a spacing of 6 m (considering a maximum speed of 20 m/s in both cases, and (3 an algorithm is presented to manage the vehicles’ priority at a traffic intersection, where the model regulates the vehicles’ acceleration (deceleration and a balance in the number of vehicles passing from each side is achieved.

  12. Disturbance Observer-Based Simple Nonlinearity Compensation for Matrix Converter Drives

    Directory of Open Access Journals (Sweden)

    Kyo-Beum Lee

    2009-01-01

    Full Text Available This paper presents a new method to compensate the nonlinearity for matrix converter drives using disturbance observer. The nonlinearity of matrix converter drives such as commutation delay, turn-on and turn-off time of switching device, and on-state switching device voltage drop is modeled by disturbance observer and compensated. The proposed method does not need any additional hardware and offline experimental measurements. The proposed compensation method is applied for high-performance induction motor drives using a 3 kW matrix converter system without a speed sensor. Simulation and experimental results show that the proposed method using disturbance observer provides good compensating characteristics.

  13. Dynamics of a delay differential equation model of hepatitis B virus infection.

    Science.gov (United States)

    Gourley, Stephen A; Kuang, Yang; Nagy, John D

    2008-04-01

    We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.

  14. A model of nonlinear strain and damage accumulation in polymer composites

    Directory of Open Access Journals (Sweden)

    A. N. Ruslantsev

    2014-01-01

    Full Text Available This paper presents a model to predict a nonlinear strain of the carbon laminate; the model is based on the relations between the theory of laminated plates and the non-linear approximation of deformation curve of unidirectional layer at the shear in the layer plane. The explicit expressions of stiffness and compliance matrices were obtained via multiplying the matrices that correspond to the elastic characteristics by the matrices, considering the non-linear properties of the laminate. The paper suggests an approximation option for the non-linear properties of the layer at the shear using an exponential function. Some considerations on damage accumulation in carbon laminates were made.

  15. Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks.

    Science.gov (United States)

    Song, Yongli; Makarov, Valeri A; Velarde, Manuel G

    2009-08-01

    A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.

  16. Interaction of few-cycle laser pulses in an isotropic nonlinear medium

    International Nuclear Information System (INIS)

    Oganesyan, D L; Vardanyan, A O

    2007-01-01

    The interaction of few-cycle laser pulses propagating in an isotropic nonlinear medium is studied theoretically. A system of nonlinear Maxwell's equations is integrated numerically with respect to time by the finite difference method. The interaction of mutually orthogonal linearly polarised 0.81-μm, 10-fs pulses is considered. Both the instant Kerr polarisation response and Raman inertial response of the medium in the nonlinear part of the medium are taken into account. The spectral shift of the probe pulse caused by the cross-action of the reference pulse is studied. The spectra of the interacting pulses are studied for different time delays between them and the shifts of these spectra are obtained as a function of the time delay. (nonlinear optical phenomena)

  17. A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.

  18. A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

    International Nuclear Information System (INIS)

    Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q

    2013-01-01

    Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field

  19. Statistics and dimension of chaos in differential delay systems

    Energy Technology Data Exchange (ETDEWEB)

    Dorizzi, B.; Grammaticos, B.; Le Berre, M.; Pomeau, Y.; Ressayre, E.; Tallet, A.

    1987-01-01

    The chaotic solution of dissipative scalar-delay-differential equations with a nonlinear feedback periodic with respect to its argument is shown to behave as a Gaussian-Markovian process in a large time scale. The short time scale is shown to be defined by the correlation time of the delayed feedback. The dimension of the chaotic attractor is shown to be approximately equal to the number of short times that are contained inside the delay.

  20. Statistics and dimension of chaos in differential delay systems

    International Nuclear Information System (INIS)

    Dorizzi, B.; Grammaticos, B.; Le Berre, M.; Pomeau, Y.; Ressayre, E.; Tallet, A.

    1987-01-01

    The chaotic solution of dissipative scalar-delay-differential equations with a nonlinear feedback periodic with respect to its argument is shown to behave as a Gaussian-Markovian process in a large time scale. The short time scale is shown to be defined by the correlation time of the delayed feedback. The dimension of the chaotic attractor is shown to be approximately equal to the number of short times that are contained inside the delay

  1. Modelling long term rockslide displacements with non-linear time-dependent relationships

    Science.gov (United States)

    De Caro, Mattia; Volpi, Giorgio; Castellanza, Riccardo; Crosta, Giovanni; Agliardi, Federico

    2015-04-01

    Rockslides undergoing rapid changes in behaviour pose major risks in alpine areas, and require careful characterization and monitoring both for civil protection and mitigation activities. In particular, these instabilities can undergo very slow movement with occasional and intermittent acceleration/deceleration stages of motion potentially leading to collapse. Therefore, the analysis of such instabilities remains a challenging issue. Rockslide displacements are strongly conditioned by hydrologic factors as suggested by correlations with groundwater fluctuations, snowmelt, with a frequently observed delay between perturbation and system reaction. The aim of this work is the simulation of the complex time-dependent behaviour of two case studies for which also a 2D transient hydrogeological simulation has been performed: Vajont rockslide (1960 to 1963) and the recent Mt. de La Saxe rockslide (2009 to 2012). Non-linear time-dependent constitutive relationships have been used to describe long-term creep deformation. Analyses have been performed using a "rheological-mechanical" approach that fits idealized models (e.g. viscoelastic, viscoplastic, elasto-viscoplastic, Burgers, nonlinear visco-plastic) to the experimental behaviour of specific materials by means of numerical constants. Bidimensional simulations were carried out using the finite difference code FLAC. Displacements time-series, available for the two landslides, show two superimposed deformation mechanisms: a creep process, leading to movements under "steady state" conditions (e.g. constant groundwater level), and a "dynamic" process, leading to an increase in displacement rate due to changes of external loads (e.g. groundwater level). For both cases sliding mass is considered as an elasto-plastic body subject to its self-weight, inertial and seepage forces varying with time according to water table fluctuation (due to snowmelt or changing in reservoir level) and derived from the previous hydrogeological

  2. Transmission Delay Modeling of Packet Communication over Digital Subscriber Line

    Directory of Open Access Journals (Sweden)

    Jiri Vodrazka

    2013-01-01

    Full Text Available Certain multimedia and voice services, such as VoIP, IPTV, etc., are significantly delay sensitive and their performance is influenced by the overall transmission delay and its variance. One of the most common solutions used in access networks are xDSL lines, especially ADSL2+ or VDSL2. Although these subscriber lines also use packet communication, there are several differences and mechanisms, which influence their resulting delay. Their delay characteristics are also dependent on the individual settings of each xDSL provider, therefore we decided to investigate this area for typical commercially available lines in Czech Republic. Based on the measured values and experiments with real ADSL2+ lines we also developed a potential modeling method, which is presented in this article as well. The parameters for packet jitter based on the generalized Pareto distribution were modeled.

  3. A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

    Science.gov (United States)

    Shi, H.; Yang, B.; Thomson, M.; Fang, H.

    2011-01-01

    This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

  4. Nonlinear unitary quantum collapse model with self-generated noise

    Science.gov (United States)

    Geszti, Tamás

    2018-04-01

    Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.

  5. Symmetries and discretizations of the O(3) nonlinear sigma model

    Energy Technology Data Exchange (ETDEWEB)

    Flore, Raphael [TPI, Universitaet Jena (Germany)

    2011-07-01

    Nonlinear sigma models possess many interesting properties like asymptotic freedom, confinement or dynamical mass generation, and hence serve as toy models for QCD and other theories. We derive a formulation of the N=2 supersymmetric extension of the O(3) nonlinear sigma model in terms of constrained field variables. Starting from this formulation, it is discussed how the model can be discretized in a way that maintains as many symmetries of the theory as possible. Finally, recent numerical results related to these discretizations are presented.

  6. PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

    Science.gov (United States)

    Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

    2017-09-01

    In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

  7. Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

    Science.gov (United States)

    Yao, Jianyong

    2018-06-01

    Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

  8. Nonlinear finite element modeling of corrugated board

    Science.gov (United States)

    A. C. Gilchrist; J. C. Suhling; T. J. Urbanik

    1999-01-01

    In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...

  9. Applications of Nonlinear Dynamics Model and Design of Complex Systems

    CERN Document Server

    In, Visarath; Palacios, Antonio

    2009-01-01

    This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

  10. Finiteness of Ricci flat supersymmetric non-linear sigma-models

    International Nuclear Information System (INIS)

    Alvarez-Gaume, L.; Ginsparg, P.

    1985-01-01

    Combining the constraints of Kaehler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear sigma-models with target space an arbitrary riemannian manifold M. We show that the constraint of N=2 supersymmetry requires that all counterterms to the metric beyond one-loop order are cohomologically trivial. It follows that such supersymmetric non-linear sigma-models defined on locally symmetric spaces are super-renormalizable and that N=4 models are on-shell ultraviolet finite to all orders of perturbation theory. (orig.)

  11. Oscillation criteria for third order delay nonlinear differential equations

    Directory of Open Access Journals (Sweden)

    E. M. Elabbasy

    2012-01-01

    via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results.

  12. Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations

    DEFF Research Database (Denmark)

    Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik

    2004-01-01

    The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...

  13. Stability and Hopf bifurcation for a delayed SLBRS computer virus model.

    Science.gov (United States)

    Zhang, Zizhen; Yang, Huizhong

    2014-01-01

    By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.

  14. Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model

    Directory of Open Access Journals (Sweden)

    Zizhen Zhang

    2014-01-01

    Full Text Available By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.

  15. Robust receding horizon control for networked and distributed nonlinear systems

    CERN Document Server

    Li, Huiping

    2017-01-01

    This book offers a comprehensive, easy-to-understand overview of receding-horizon control for nonlinear networks. It presents novel general strategies that can simultaneously handle general nonlinear dynamics, system constraints, and disturbances arising in networked and large-scale systems and which can be widely applied. These receding-horizon-control-based strategies can achieve sub-optimal control performance while ensuring closed-loop stability: a feature attractive to engineers. The authors address the problems of networked and distributed control step-by-step, gradually increasing the level of challenge presented. The book first introduces the state-feedback control problems of nonlinear networked systems and then studies output feedback control problems. For large-scale nonlinear systems, disturbance is considered first, then communication delay separately, and lastly the simultaneous combination of delays and disturbances. Each chapter of this easy-to-follow book not only proposes and analyzes novel ...

  16. A cash flow oriented EOQ model under permissible delay in payments

    African Journals Online (AJOL)

    A cash flow oriented EOQ model under permissible delay in payments. RP Tripathi, SS Misra, HS Shukla. Abstract. This study presents an inventory model to determine an optimal ordering policy for non-deteriorating items and timedependent demand rate with delay in payments permitted by the supplier under inflation and ...

  17. Rich dynamics of discrete delay ecological models

    International Nuclear Information System (INIS)

    Peng Mingshu

    2005-01-01

    We study multiple bifurcations and chaotic behavior of a discrete delay ecological model. New form of chaos for the 2-D map is observed: the combination of potential period doubling and reverse period-doubling leads to cascading bubbles

  18. Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

    Science.gov (United States)

    Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

    2012-01-01

    Purpose: The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F[subscript 0]) during anterior-posterior stretching. Method: Three materially linear and 3 materially nonlinear models were…

  19. Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

    Science.gov (United States)

    Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

    2009-01-01

    Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

  20. Modal model for the nonlinear multimode Rayleigh endash Taylor instability

    International Nuclear Information System (INIS)

    Ofer, D.; Alon, U.; Shvarts, D.; McCrory, R.L.; Verdon, C.P.

    1996-01-01

    A modal model for the Rayleigh endash Taylor (RT) instability, applicable at all stages of the flow, is introduced. The model includes a description of nonlinear low-order mode coupling, mode growth saturation, and post-saturation mode coupling. It is shown to significantly extend the range of applicability of a previous model proposed by Haan, to cases where nonlinear mode generation is important. Using the new modal model, we study the relative importance of mode coupling at late nonlinear stages and resolve the difference between cases in which mode generation assumes a dominant role, leading to the late time inverse cascade of modes and loss of memory of initial conditions, and cases where mode generation is not important and memory of initial conditions is retained. Effects of finite density ratios (Atwood number A<1) are also included in the model and the difference between various measures of the mixing zone penetration depth for A<1 is discussed. copyright 1996 American Institute of Physics

  1. Convex models and probabilistic approach of nonlinear fatigue failure

    International Nuclear Information System (INIS)

    Qiu Zhiping; Lin Qiang; Wang Xiaojun

    2008-01-01

    This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach

  2. Analysis, control and design of speed control of electric vehicles delayed model

    DEFF Research Database (Denmark)

    Khooban, Mohammad-Hassan; ShaSadeghi, Mokhtar; Niknam, Taher

    2017-01-01

    The purpose of this study is to suggest an optimal multi-objective fuzzy fractional-order PIλDμPIλDμ controller (MOFFOPID) for the speed control of EV systems with time-delay. It is presumed that while the EV is in movement, the armature winding resistance of the direct current (DC) motor varies...... controller. Finally, the experimental results based on a TMS320F28335 DSP are implemented on a DC motor to verify the effectiveness of the proposed MOFFOPID controller in controlling the speed of the DC motor which has non-linear features. The results of the simulation confirm the desirable performance...

  3. Bifurcation and stability analysis of a nonlinear milling process

    Science.gov (United States)

    Weremczuk, Andrzej; Rusinek, Rafal; Warminski, Jerzy

    2018-01-01

    Numerical investigations of milling operations dynamics are presented in this paper. A two degree of freedom nonlinear model is used to study workpiece-tool vibrations. The analyzed model takes into account both flexibility of the tool and the workpiece. The dynamics of the milling process is described by the discontinuous ordinary differential equation with time delay, which can cause process instability. First, stability lobes diagrams are created on the basis of the parameters determined in impact test of an end mill and workpiece. Next, the bifurcations diagrams are performed for different values of rotational speeds.

  4. Calibration of the Nonlinear Accelerator Model at the Diamond Storage Ring

    CERN Document Server

    Bartolini, Riccardo; Rowland, James; Martin, Ian; Schmidt, Frank

    2010-01-01

    The correct implementation of the nonlinear ring model is crucial to achieve the top performance of a synchrotron light source. Several dynamics quantities can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these methods are based on the analysis of turn-by-turn data of excited betatron oscillations. We present the experimental results of the campaign of measurements carried out at the Diamond. A combination of Frequency Map Analysis (FMA) and detuning with momentum measurements has allowed a precise calibration of the nonlinear model capable of reproducing the nonlinear beam dynamics in the storage ring

  5. Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays

    Directory of Open Access Journals (Sweden)

    T. S. Doan

    2012-01-01

    Full Text Available We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.

  6. Modeling of nonlinear responses for reciprocal transducers involving polarization switching

    DEFF Research Database (Denmark)

    Willatzen, Morten; Wang, Linxiang

    2007-01-01

    Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...

  7. Nonlinear Jaynes–Cummings model for two interacting two-level atoms

    International Nuclear Information System (INIS)

    Santos-Sánchez, O de los; González-Gutiérrez, C; Récamier, J

    2016-01-01

    In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space. (paper)

  8. Finger tapping movements of Parkinson's disease patients automatically rated using nonlinear delay differential equations.

    Science.gov (United States)

    Lainscsek, C; Rowat, P; Schettino, L; Lee, D; Song, D; Letellier, C; Poizner, H

    2012-03-01

    Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p<0.0015) correlation between them.

  9. System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time

    DEFF Research Database (Denmark)

    Sun, Zhen; Yang, Zhenyu

    2011-01-01

    An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent....

  10. Langevin approach to synchronization of hyperchaotic time-delay dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Budini, Adrian A [Consejo Nacional de Investigaciones CientIficas y Tecnicas, Centro Atomico Bariloche, Av. E Bustillo Km 9.5, (8400) Bariloche (Argentina); Consortium of the Americas for Interdisciplinary Science and Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131 (United States)

    2008-11-07

    In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar nonlinear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical properties of a class of hyperchaotic attractors can be reproduced with a linear Langevin equation, defined by replacing the nonlinear delay force by a delta-correlated noise. Therefore, the synchronization phenomenon can be analytically characterized by a set of coupled Langevin equations. We apply this formalism to study anticipated synchronization dynamics subject to external noise fluctuations as well as for characterizing the effects of parameter mismatch in a hyperchaotic communication scheme. The same procedure is applied to second-order differential delay equations associated with synchronization in electro-optical devices. In all cases, the departure with respect to perfect synchronization is measured through a similarity function. Numerical simulations in discrete maps associated with the hyperchaotic dynamics support the formalism.

  11. Measuring and Modelling Delays in Robot Manipulators for Temporally Precise Control using Machine Learning

    DEFF Research Database (Denmark)

    Andersen, Thomas Timm; Amor, Heni Ben; Andersen, Nils Axel

    2015-01-01

    and separate. In this paper, we present a data-driven methodology for separating and modelling inherent delays during robot control. We show how both actuation and response delays can be modelled using modern machine learning methods. The resulting models can be used to predict the delays as well...

  12. Predictor-based stabilization for chained form systems with input time delay

    Directory of Open Access Journals (Sweden)

    Mnif Faïçal

    2016-12-01

    Full Text Available This note addresses the stabilization problem of nonlinear chained-form systems with input time delay. We first employ the so-called σ-process transformation that renders the feedback system under a linear form. We introduce a particular transformation to convert the original system into a delay-free system. Finally, we apply a state feedback control, which guarantees a quasi-exponential stabilization to all the system states, which in turn converge exponentially to zero. Then we employ the so-called -type control to achieve a quasi-exponential stabilization of the subsequent system. A simulation example illustrated on the model of a wheeled mobile robot is provided to demonstrate the effectiveness of the proposed approach.

  13. Lattice Boltzmann model for high-order nonlinear partial differential equations.

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  14. Lattice Boltzmann model for high-order nonlinear partial differential equations

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  15. Nonlinear interaction model of subsonic jet noise.

    Science.gov (United States)

    Sandham, Neil D; Salgado, Adriana M

    2008-08-13

    Noise generation in a subsonic round jet is studied by a simplified model, in which nonlinear interactions of spatially evolving instability modes lead to the radiation of sound. The spatial mode evolution is computed using linear parabolized stability equations. Nonlinear interactions are found on a mode-by-mode basis and the sound radiation characteristics are determined by solution of the Lilley-Goldstein equation. Since mode interactions are computed explicitly, it is possible to find their relative importance for sound radiation. The method is applied to a single stream jet for which experimental data are available. The model gives Strouhal numbers of 0.45 for the most amplified waves in the jet and 0.19 for the dominant sound radiation. While in near field axisymmetric and the first azimuthal modes are both important, far-field sound is predominantly axisymmetric. These results are in close correspondence with experiment, suggesting that the simplified model is capturing at least some of the important mechanisms of subsonic jet noise.

  16. Nonlinear price impact from linear models

    Science.gov (United States)

    Patzelt, Felix; Bouchaud, Jean-Philippe

    2017-12-01

    The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators, and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales (Patzelt and Bouchaud 2017 arXiv:1706.04163). Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear ‘propagator’ models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.

  17. Modeling and nonlinear heading control for sailing yachts

    DEFF Research Database (Denmark)

    Xiao, Lin; Jouffroy, Jerome

    2014-01-01

    This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen’s compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also...

  18. Modeling and nonlinear heading control for sailing yachts

    DEFF Research Database (Denmark)

    Xiao, Lin; Jouffroy, Jerome

    2011-01-01

    This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear 4-DOF dynamic model for a sailing yacht, including roll. Starting from this model, we then design...

  19. Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model

    Directory of Open Access Journals (Sweden)

    Yacouba Simporé

    2016-01-01

    Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.

  20. Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses

    DEFF Research Database (Denmark)

    Fasil, Muhammed; Mijatovic, Nenad; Jensen, Bogi Bech

    2017-01-01

    The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless DC (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modelling fractional-slot machines. The inaccuracy of phase variable mod...... on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model....... of fractional-slot machines can be attributed to considerable armature flux harmonics, which causes an increased core loss. This study proposes a nonlinear phase variable model of PMBLDC motor that considers the core losses induced in the stator and the rotor. The core loss model is developed based...

  1. Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.

    Science.gov (United States)

    Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J

    2016-10-03

    Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

  2. Applicability of linear and non-linear potential flow models on a Wavestar float

    DEFF Research Database (Denmark)

    Bozonnet, Pauline; Dupin, Victor; Tona, Paolino

    2017-01-01

    as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...

  3. Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

    Science.gov (United States)

    Li, Guang

    2017-01-01

    This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

  4. Model Predictive Control of a Nonlinear System with Known Scheduling Variable

    DEFF Research Database (Denmark)

    Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

    2012-01-01

    Model predictive control (MPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Consequently...... the control problem of the nonlinear system is simplied into a quadratic programming. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon....

  5. Noise-sustained fluctuations in stochastic dynamics with a delay.

    Science.gov (United States)

    D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca

    2012-04-01

    Delayed responses to external drivers are ubiquitous in environmental, social, and biological processes. Delays may induce oscillations, Hopf bifurcations, and instabilities in deterministic systems even in the absence of nonlinearities. Despite recent advances in the study of delayed stochastic differential equations, the interaction of random drivers with delays remains poorly understood. In particular, it is unclear whether noise-induced behaviors may emerge from these interactions. Here we show that noise may enhance and sustain transient periodic oscillations inherent to deterministic delayed systems. We investigate the conditions conducive to the emergence and disappearance of these dynamics in a linear system in the presence of both additive and multiplicative noise.

  6. Multi-atom Jaynes-Cummings model with nonlinear effects

    International Nuclear Information System (INIS)

    Aleixo, Armando Nazareno Faria; Balantekin, Akif Baha; Ribeiro, Marco Antonio Candido

    2001-01-01

    The standard Jaynes-Cummings (JC) model and its extensions, normally used in quantum optics, idealizes the interaction of matter with electromagnetic radiation by a simple Hamiltonian of a two-level atom coupled to a single bosonic mode. This Hamiltonian has a fundamental importance to the field of quantum optics and it is a central ingredient in the quantized description of any optical system involving the interaction between light and atoms. The JC Hamiltonian defines a molecule, a composite system formed from the coupling of a two-state system and a quantized harmonic oscillator. For this Hamiltonian, mostly the single-particle situation has been studied. This model can also be extended for the situation where one has N two-level systems, which interact only with the electromagnetic radiation. In this case the effects of the spatial distribution of the particles it is not taken into account and the spin angular momentum S-circumflex i of each particle contributes to form a total angular momentum J-circumflex of the system. When one considers the effects due to the spatial variation in the field intensity in a nonlinear medium it is necessary to further add a Kerr term to the standard JC Hamiltonian. This kind of nonlinear JC Hamiltonian is used in the study of micro masers. Another nonlinear variant of the JC model takes the coupling between matter and the radiation to depend on the intensity of the electromagnetic field. This model is interesting since this kind of interaction means that effectively the coupling is proportional to the amplitude of the field representing a very simple case of a nonlinear interaction corresponding to a more realistic physical situation. In this work we solve exactly the problem of the interaction of a N two-level atoms with an electromagnetic radiation when nonlinear effects due to the spatial variation in the field intensity in a nonlinear Kerr medium and the dependence on the intensity of the electromagnetic field on the matter

  7. A mathematical model of a crocodilian population using delay-differential equations.

    Science.gov (United States)

    Gallegos, Angela; Plummer, Tenecia; Uminsky, David; Vega, Cinthia; Wickman, Clare; Zawoiski, Michael

    2008-11-01

    The crocodilia have multiple interesting characteristics that affect their population dynamics. They are among several reptile species which exhibit temperature-dependent sex determination (TSD) in which the temperature of egg incubation determines the sex of the hatchlings. Their life parameters, specifically birth and death rates, exhibit strong age-dependence. We develop delay-differential equation (DDE) models describing the evolution of a crocodilian population. In using the delay formulation, we are able to account for both the TSD and the age-dependence of the life parameters while maintaining some analytical tractability. In our single-delay model we also find an equilibrium point and prove its local asymptotic stability. We numerically solve the different models and investigate the effects of multiple delays on the age structure of the population as well as the sex ratio of the population. For all models we obtain very strong agreement with the age structure of crocodilian population data as reported in Smith and Webb (Aust. Wild. Res. 12, 541-554, 1985). We also obtain reasonable values for the sex ratio of the simulated population.

  8. Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

    Science.gov (United States)

    Zhang, Yu; Jiang, Jack J.

    2008-09-01

    Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

  9. Delay-independent stability of genetic regulatory networks.

    Science.gov (United States)

    Wu, Fang-Xiang

    2011-11-01

    Genetic regulatory networks can be described by nonlinear differential equations with time delays. In this paper, we study both locally and globally delay-independent stability of genetic regulatory networks, taking messenger ribonucleic acid alternative splicing into consideration. Based on nonnegative matrix theory, we first develop necessary and sufficient conditions for locally delay-independent stability of genetic regulatory networks with multiple time delays. Compared to the previous results, these conditions are easy to verify. Then we develop sufficient conditions for global delay-independent stability for genetic regulatory networks. Compared to the previous results, this sufficient condition is less conservative. To illustrate theorems developed in this paper, we analyze delay-independent stability of two genetic regulatory networks: a real-life repressilatory network with three genes and three proteins, and a synthetic gene regulatory network with five genes and seven proteins. The simulation results show that the theorems developed in this paper can effectively determine the delay-independent stability of genetic regulatory networks.

  10. Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays

    Directory of Open Access Journals (Sweden)

    Ravi Agarwal

    2018-05-01

    Full Text Available One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable. In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability of equilibrium of nonlinear Caputo fractional neural networks with time dependent transmission delays, time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. The cases of time varying Lipschitz coefficients as well as nonLipschitz activation functions are studied. We illustrate our theory on particular nonlinear Caputo fractional neural networks.

  11. A direct method for numerical solution of a class of nonlinear Volterra integro-differential equations and its application to the nonlinear fission and fusion reactor kinetics

    International Nuclear Information System (INIS)

    Nakahara, Yasuaki; Ise, Takeharu; Kobayashi, Kensuke; Itoh, Yasuyuki

    1975-12-01

    A new method has been developed for numerical solution of a class of nonlinear Volterra integro-differential equations with quadratic nonlinearity. After dividing the domain of the variable into subintervals, piecewise approximations are applied in the subintervals. The equation is first integrated over a subinterval to obtain the piecewise equation, to which six approximate treatments are applied, i.e. fully explicit, fully implicit, Crank-Nicolson, linear interpolation, quadratic and cubic spline. The numerical solution at each time step is obtained directly as a positive root of the resulting algebraic quadratic equation. The point reactor kinetics with a ramp reactivity insertion, linear temperature feedback and delayed neutrons can be described by one of this type of nonlinear Volterra integro-differential equations. The algorithm is applied to the Argonne benchmark problem and a model problem for a fast reactor without delayed neutrons. The fully implicit method has been found to be unconditionally stable in the sense that it always gives the positive real roots. The cubic spline method is divergent, and the other four methods are intermediate in between. From the estimation of the stability, convergency, accuracy and CPU time, it is concluded that the Crank-Nicolson method is best, then the linear interpolation method comes closely next to it. Discussions are also made on the possibility of applying the algorithm to the fusion reactor kinetics in the form of a nonlinear partial differential equation. (auth.)

  12. Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

    Science.gov (United States)

    Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

    2017-05-01

    We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

  13. Nonlinear model of a rotating hub-beams structure: Equations of motion

    Science.gov (United States)

    Warminski, Jerzy

    2018-01-01

    Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

  14. Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

    Directory of Open Access Journals (Sweden)

    YanBin Liu

    2017-01-01

    Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.

  15. Nonlinear optical model for strip plasmonic waveguides

    DEFF Research Database (Denmark)

    Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei

    2016-01-01

    This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core...... significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett. 41, 317 (2016...... approaches. (C) 2016 Optical Society of America...

  16. Sphaleron in a non-linear sigma model

    International Nuclear Information System (INIS)

    Sogo, Kiyoshi; Fujimoto, Yasushi.

    1989-08-01

    We present an exact classical saddle point solution in a non-linear sigma model. It has a topological charge 1/2 and mediates the vacuum transition. The quantum fluctuations and the transition rate are also examined. (author)

  17. Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.

    Science.gov (United States)

    Shang, Xituan; Yen, Michael R T; Gaber, M Waleed

    2010-06-01

    The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.

  18. Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

    Science.gov (United States)

    Vila, J.; Fernández-Sáez, J.; Zaera, R.

    2018-04-01

    In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

  19. Neuronal model with distributed delay: analysis and simulation study for gamma distribution memory kernel.

    Science.gov (United States)

    Karmeshu; Gupta, Varun; Kadambari, K V

    2011-06-01

    A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen-Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV(t))((ISI)) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.

  20. Static aeroelastic analysis including geometric nonlinearities based on reduced order model

    Directory of Open Access Journals (Sweden)

    Changchuan Xie

    2017-04-01

    Full Text Available This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model (ROM. The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method (FEM especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite element (MFE method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM. Structure and aerodynamics can be coupled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

  1. Non-linear characterisation of the physical model of an ancient masonry bridge

    International Nuclear Information System (INIS)

    Fragonara, L Zanotti; Ceravolo, R; Matta, E; Quattrone, A; De Stefano, A; Pecorelli, M

    2012-01-01

    This paper presents the non-linear investigations carried out on a scaled model of a two-span masonry arch bridge. The model has been built in order to study the effect of the central pile settlement due to riverbank erosion. Progressive damage was induced in several steps by applying increasing settlements at the central pier. For each settlement step, harmonic shaker tests were conducted under different excitation levels, this allowing for the non-linear identification of the progressively damaged system. The shaker tests have been performed at resonance with the modal frequency of the structure, which were determined from a previous linear identification. Estimated non-linearity parameters, which result from the systematic application of restoring force based identification algorithms, can corroborate models to be used in the reassessment of existing structures. The method used for non-linear identification allows monitoring the evolution of non-linear parameters or indicators which can be used in damage and safety assessment.

  2. Model reduction of systems with localized nonlinearities.

    Energy Technology Data Exchange (ETDEWEB)

    Segalman, Daniel Joseph

    2006-03-01

    An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.

  3. Distance Dependent Model for the Delay Power Spectrum of In-room Radio Channels

    DEFF Research Database (Denmark)

    Steinböck, Gerhard; Pedersen, Troels; Fleury, Bernard Henri

    2013-01-01

    A model based on experimental observations of the delay power spectrum in closed rooms is proposed. The model includes the distance between the transmitter and the receiver as a parameter which makes it suitable for range based radio localization. The experimental observations motivate the proposed...... model of the delay power spectrum with a primary (early) component and a reverberant component (tail). The primary component is modeled as a Dirac delta function weighted according to an inverse distance power law (d-n). The reverberant component is an exponentially decaying function with onset equal...... to the propagation time between transmitter and receiver. Its power decays exponentially with distance. The proposed model allows for the prediction of e.g. the path loss, mean delay, root mean squared (rms) delay spread, and kurtosis versus the distance. The model predictions are validated by measurements...

  4. Research on nonlinear stochastic dynamical price model

    International Nuclear Information System (INIS)

    Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng

    2008-01-01

    In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies

  5. Novel images extraction model using improved delay vector variance feature extraction and multi-kernel neural network for EEG detection and prediction.

    Science.gov (United States)

    Ge, Jing; Zhang, Guoping

    2015-01-01

    Advanced intelligent methodologies could help detect and predict diseases from the EEG signals in cases the manual analysis is inefficient available, for instance, the epileptic seizures detection and prediction. This is because the diversity and the evolution of the epileptic seizures make it very difficult in detecting and identifying the undergoing disease. Fortunately, the determinism and nonlinearity in a time series could characterize the state changes. Literature review indicates that the Delay Vector Variance (DVV) could examine the nonlinearity to gain insight into the EEG signals but very limited work has been done to address the quantitative DVV approach. Hence, the outcomes of the quantitative DVV should be evaluated to detect the epileptic seizures. To develop a new epileptic seizure detection method based on quantitative DVV. This new epileptic seizure detection method employed an improved delay vector variance (IDVV) to extract the nonlinearity value as a distinct feature. Then a multi-kernel functions strategy was proposed in the extreme learning machine (ELM) network to provide precise disease detection and prediction. The nonlinearity is more sensitive than the energy and entropy. 87.5% overall accuracy of recognition and 75.0% overall accuracy of forecasting were achieved. The proposed IDVV and multi-kernel ELM based method was feasible and effective for epileptic EEG detection. Hence, the newly proposed method has importance for practical applications.

  6. Singular perturbation methods for nonlinear dynamic systems with time delays

    International Nuclear Information System (INIS)

    Hu, H.Y.; Wang, Z.H.

    2009-01-01

    This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.

  7. A Comparative Study Of Stock Price Forecasting Using Nonlinear Models

    Directory of Open Access Journals (Sweden)

    Diteboho Xaba

    2017-03-01

    Full Text Available This study compared the in-sample forecasting accuracy of three forecasting nonlinear models namely: the Smooth Transition Regression (STR model, the Threshold Autoregressive (TAR model and the Markov-switching Autoregressive (MS-AR model. Nonlinearity tests were used to confirm the validity of the assumptions of the study. The study used model selection criteria, SBC to select the optimal lag order and for the selection of appropriate models. The Mean Square Error (MSE, Mean Absolute Error (MAE and Root Mean Square Error (RMSE served as the error measures in evaluating the forecasting ability of the models. The MS-AR models proved to perform well with lower error measures as compared to LSTR and TAR models in most cases.

  8. Model Updating Nonlinear System Identification Toolbox, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...

  9. Dynamical Analysis of SIR Epidemic Models with Distributed Delay

    Directory of Open Access Journals (Sweden)

    Wencai Zhao

    2013-01-01

    Full Text Available SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction number R is got. In order to study the important role of vaccination to prevent diseases, the model with distributed delay under impulsive vaccination is formulated. And the sufficient conditions of globally asymptotic stability of “infection-free” periodic solution and the permanence of the model are obtained by using Floquet’s theorem, small-amplitude perturbation skills, and comparison theorem. Lastly, numerical simulation is presented to illustrate our main conclusions that vaccination has significant effects on the dynamical behaviors of the model. The results can provide effective tactic basis for the practical infectious disease prevention.

  10. Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination

    International Nuclear Information System (INIS)

    Meng Xinzhu; Jiao Jianjun; Chen Lansun

    2009-01-01

    Since the investigation of impulsive delay differential equations is beginning, the literature on delay epidemic models with pulse vaccination is not extensive. In this paper, we propose a new SEIRS epidemic disease model with two profitless delays and vertical transmission, and analyze the dynamics behaviors of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain a 'infection-free' periodic solution, further, show that the 'infection-free' periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using a new modeling method, we obtain sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delays, pulse vaccination and vertical transmission can bring different effects on the dynamics behaviors of the model by numerical analysis. Our results also show the delays are 'profitless'. In this paper, the main feature is to introduce two discrete time delays, vertical transmission and impulse into SEIRS epidemic model and to give pulse vaccination strategies.

  11. Symbolic-computation study of the perturbed nonlinear Schrodinger model in inhomogeneous optical fibers

    International Nuclear Information System (INIS)

    Tian Bo; Gao Yitian

    2005-01-01

    A realistic, inhomogeneous fiber in the optical communication systems can be described by the perturbed nonlinear Schrodinger model (also named as the normalized nonlinear Schrodinger model with periodically varying coefficients, dispersion managed nonlinear Schrodinger model or nonlinear Schrodinger model with variable coefficients). Hereby, we extend to this model a direct method, perform symbolic computation and obtain two families of the exact, analytic bright-solitonic solutions, with or without the chirp respectively. The parameters addressed include the shape of the bright soliton, soliton amplitude, inverse width of the soliton, chirp, frequency, center of the soliton and center of the phase of the soliton. Of optical and physical interests, we discuss some previously-published special cases of our solutions. Those solutions could help the future studies on the optical communication systems. ms

  12. Model-free inference of direct network interactions from nonlinear collective dynamics.

    Science.gov (United States)

    Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

    2017-12-19

    The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

  13. A non-linear model of economic production processes

    Science.gov (United States)

    Ponzi, A.; Yasutomi, A.; Kaneko, K.

    2003-06-01

    We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

  14. A nonlinear complementarity approach for the national energy modeling system

    International Nuclear Information System (INIS)

    Gabriel, S.A.; Kydes, A.S.

    1995-01-01

    The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP

  15. Nonlinear transfer of elements from soil to plants: impact on radioecological modeling

    Energy Technology Data Exchange (ETDEWEB)

    Tuovinen, Tiina S.; Kolehmainen, Mikko; Roivainen, Paeivi; Kumlin, Timo; Makkonen, Sari; Holopainen, Toini; Juutilainen, Jukka [University of Eastern Finland, Department of Environmental and Biological Sciences, P.O. Box 1627, Kuopio (Finland)

    2016-08-15

    In radioecology, transfer of radionuclides from soil to plants is typically described by a concentration ratio (CR), which assumes linearity of transfer with soil concentration. Nonlinear uptake is evidenced in many studies, but it is unclear how it should be taken into account in radioecological modeling. In this study, a conventional CR-based linear model, a nonlinear model derived from observed uptake into plants, and a new simple model based on the observation that nonlinear uptake leads to a practically constant concentration in plant tissues are compared. The three models were used to predict transfer of {sup 234}U, {sup 59}Ni and {sup 210}Pb into spruce needles. The predictions of the nonlinear and the new model were essentially similar. In contrast, plant radionuclide concentration was underestimated by the linear model when the total element concentration in soil was relatively low, but within the range commonly observed in nature. It is concluded that the linear modeling could easily be replaced by a new approach that more realistically reflects the true processes involved in the uptake of elements into plants. The new modeling approach does not increase the complexity of modeling in comparison with CR-based linear models, and data needed for model parameters (element concentrations) are widely available. (orig.)

  16. Modelling and tuning for a time-delayed vibration absorber with friction

    Science.gov (United States)

    Zhang, Xiaoxu; Xu, Jian; Ji, Jinchen

    2018-06-01

    This paper presents an integrated analytical and experimental study to the modelling and tuning of a time-delayed vibration absorber (TDVA) with friction. In system modelling, this paper firstly applies the method of averaging to obtain the frequency response function (FRF), and then uses the derived FRF to evaluate the fitness of different friction models. After the determination of the system model, this paper employs the obtained FRF to evaluate the vibration absorption performance with respect to tunable parameters. A significant feature of the TDVA with friction is that its stability is dependent on the excitation parameters. To ensure the stability of the time-delayed control, this paper defines a sufficient condition for stability estimation. Experimental measurements show that the dynamic response of the TDVA with friction can be accurately predicted and the time-delayed control can be precisely achieved by using the modelling and tuning technique provided in this paper.

  17. A high-resolution programmable Vernier delay generator based on carry chains in FPGA.

    Science.gov (United States)

    Cui, Ke; Li, Xiangyu; Zhu, Rihong

    2017-06-01

    This paper presents an architecture of a high-resolution delay generator implemented in a single field programmable gate array chip by exploiting the method of utilizing dedicated carry chains. It serves as the core component in various physical instruments. The proposed delay generator contains the coarse delay step and the fine delay step to guarantee both large dynamic range and high resolution. The carry chains are organized in the Vernier delay loop style to fulfill the fine delay step with high precision and high linearity. The delay generator was implemented in the EP3SE110F1152I3 Stratix III device from Altera on a self-designed test board. Test results show that the obtained resolution is 38.6 ps, and the differential nonlinearity/integral nonlinearity is in the range of [-0.18 least significant bit (LSB), 0.24 LSB]/(-0.02 LSB, 0.01 LSB) under the nominal supply voltage of 1100 mV and environmental temperature of 20  ° C. The delay generator is rather efficient concerning resource cost, which uses only 668 look-up tables and 146 registers in total.

  18. A high-resolution programmable Vernier delay generator based on carry chains in FPGA

    Science.gov (United States)

    Cui, Ke; Li, Xiangyu; Zhu, Rihong

    2017-06-01

    This paper presents an architecture of a high-resolution delay generator implemented in a single field programmable gate array chip by exploiting the method of utilizing dedicated carry chains. It serves as the core component in various physical instruments. The proposed delay generator contains the coarse delay step and the fine delay step to guarantee both large dynamic range and high resolution. The carry chains are organized in the Vernier delay loop style to fulfill the fine delay step with high precision and high linearity. The delay generator was implemented in the EP3SE110F1152I3 Stratix III device from Altera on a self-designed test board. Test results show that the obtained resolution is 38.6 ps, and the differential nonlinearity/integral nonlinearity is in the range of [-0.18 least significant bit (LSB), 0.24 LSB]/(-0.02 LSB, 0.01 LSB) under the nominal supply voltage of 1100 mV and environmental temperature of 2 0°C. The delay generator is rather efficient concerning resource cost, which uses only 668 look-up tables and 146 registers in total.

  19. Influence of delayed neutron parameter calculation accuracy on results of modeled WWER scram experiments

    International Nuclear Information System (INIS)

    Artemov, V.G.; Gusev, V.I.; Zinatullin, R.E.; Karpov, A.S.

    2007-01-01

    Using modeled WWER cram rod drop experiments, performed at the Rostov NPP, as an example, the influence of delayed neutron parameters on the modeling results was investigated. The delayed neutron parameter values were taken from both domestic and foreign nuclear databases. Numerical modeling was carried out on the basis of SAPFIR 9 5andWWERrogram package. Parameters of delayed neutrons were acquired from ENDF/B-VI and BNAB-78 validated data files. It was demonstrated that using delay fraction data from different databases in reactivity meters led to significantly different reactivity results. Based on the results of numerically modeled experiments, delayed neutron parameters providing the best agreement between calculated and measured data were selected and recommended for use in reactor calculations (Authors)

  20. Hopf bifurcation in a delayed reaction-diffusion-advection population model

    Science.gov (United States)

    Chen, Shanshan; Lou, Yuan; Wei, Junjie

    2018-04-01

    In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.