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Shadan Sadigh Behzadi
2011-12-01
Full Text Available In this paper, Adomian decomposition method (ADM and homotopy analysis method (HAM are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind$(FVFIE-2$. we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy Volterra-Fredholm integral equation. Also, the existence and uniqueness of the solution and convergence of the proposed methods are proved. Examples is given and the results reveal that homotopy analysis method is very effective and simple compared with the Adomian decomposition method.
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Emran Tohidi
2014-01-01
Full Text Available We are concerned with the extension of a Legendre spectral method to the numerical solution of nonlinear systems of Volterra integral equations of the second kind. It is proved theoretically that the proposed method converges exponentially provided that the solution is sufficiently smooth. Also, three biological systems which are known as the systems of Lotka-Volterra equations are approximately solved by the presented method. Numerical results confirm the theoretical prediction of the exponential rate of convergence.
Xu, Run; Ma, Xiangting
2017-01-01
In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.
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Sohrab Bazm
2016-11-01
Full Text Available Alternative Legendre polynomials (ALPs are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.
GLOBAL SOLUTIONS OF SYSTEMS OF NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
陈芳启; 陈予恕
2001-01-01
The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained,which extend the related results for this class of equations on a finite interval with a finite number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.
Wei, Yunxia; Chen, Yanping; Shi, Xiulian; Zhang, Yuanyuan
2016-01-01
We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text] (d denotes the space dimensions) as the collocation points. The error analysis in [Formula: see text]-norm and [Formula: see text]-norm theoretically justifies the exponential convergence of spectral collocation method in multidimensional space. We give two numerical examples in order to illustrate the validity of the proposed Jacobi spectral collocation method.
Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces
Institute of Scientific and Technical Information of China (English)
CHEN Fangqi; TIAN Ruilan
2005-01-01
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
Asymptotically periodic solutions of Volterra integral equations
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Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
Integrability of some generalized Lotka - Volterra systems
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Bountis, T.C.; Bier, M.; Hijmans, J.
1983-08-08
Several integrable systems of nonlinear ordinary differential equations of the Lotka-Volterra type are identified by the Painleve property and completely integrated. One such integrable case of N first order ode's is found, with N - 2 free parameters and N arbitrary. The concept of integrability of a general dynamical system, not necessarily derived from a hamiltonian, is also discussed.
Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations
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E. Messina
2008-01-01
Full Text Available We consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj, i=0,1,2,…, where fj(x (j=0,…,i are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.
Inequalities applicable to retarded Volterra integral equations
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B. G. Pachpatte
2004-12-01
Full Text Available The main objective of this paper is to establish explicit bounds on certain integral inequialities which can be used as tools in the study of certain classes of retarded Volterra integral equations.
Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain
Zhang, B.; Billings, S. A.
2017-02-01
The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.
Adomian Method for Solving Fuzzy Fredholm-Volterra Integral Equations
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M. Barkhordari Ahmadi
2013-09-01
Full Text Available In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.
On a Volterra Stieltjes integral equation
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P. T. Vaz
1990-01-01
Full Text Available The paper deals with a study of linear Volterra integral equations involving Lebesgue-Stieltjes integrals in two independent variables. The authors prove an existence theorem using the Banach fixed-point principle. An explicit example is also considered.
Integrable deformations of Lotka-Volterra systems
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Ballesteros, Angel, E-mail: angelb@ubu.es [Departamento de Fisica, Universidad de Burgos, 09001 Burgos (Spain); Blasco, Alfonso, E-mail: ablasco@ubu.es [Departamento de Fisica, Universidad de Burgos, 09001 Burgos (Spain); Musso, Fabio, E-mail: fmusso@ubu.es [Departamento de Fisica, Universidad de Burgos, 09001 Burgos (Spain)
2011-09-05
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map Δ{sup (2)} that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found. -- Highlights: → A new Poisson-Lie approach to the integrability of Lotka-Volterra system is given. → New integrable deformations of the 3D Lotka-Volterra system are obtained. → Integrable Lotka-Volterra-type equations in 3N dimensions are deduced.
Reduced Complexity Volterra Models for Nonlinear System Identification
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Hacıoğlu Rıfat
2001-01-01
Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.
An integrable Poisson map generated from the eigenvalue problem of the Lotka-Volterra hierarchy
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Wu Yongtang [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Wang Hongye [Department of Mathematics, Zhengzhou University, Henan (China); Du Dianlou [Department of Mathematics, Zhengzhou University, Henan (China)]. E-mail: ddl@zzu.edu.cn
2002-05-03
A 3x3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2x2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation. (author)
An approximation scheme for optimal control of Volterra integral equations
Belbas, S. A.
2006-01-01
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential equations. The resulting approximating problems can then be solved by dynamic programming methods for ODE controlled systems. Other, straightforward versions of dynamic programming, are not applicable to Volterra integral equations. We also derive the connection b...
Nonlinear identification of MDOF systems using Volterra series approximation
Prawin, J.; Rao, A. Rama Mohan
2017-02-01
Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Meanwhile, the presence of non-linearity in the system can lead to a wide range of structural behavior, for example, jumps, limit cycles, internal resonances, modal coupling, super and sub-harmonic resonances, etc. In this paper, we present a Volterra series approximation approach based on the adaptive filter concept for nonlinear identification of multi-degree of freedom systems, without sacrificing the benefits associated with the traditional Volterra series approach. The effectiveness of the proposed approach is demonstrated using two classical single degrees of freedom systems (breathing crack problem and Duffing Holmes oscillator) and later we extend to multi-degree of freedom systems.
Nonlinear stochastic system identification of skin using volterra kernels.
Chen, Yi; Hunter, Ian W
2013-04-01
Volterra kernel stochastic system identification is a technique that can be used to capture and model nonlinear dynamics in biological systems, including the nonlinear properties of skin during indentation. A high bandwidth and high stroke Lorentz force linear actuator system was developed and used to test the mechanical properties of bulk skin and underlying tissue in vivo using a non-white input force and measuring an output position. These short tests (5 s) were conducted in an indentation configuration normal to the skin surface and in an extension configuration tangent to the skin surface. Volterra kernel solution methods were used including a fast least squares procedure and an orthogonalization solution method. The practical modifications, such as frequency domain filtering, necessary for working with low-pass filtered inputs are also described. A simple linear stochastic system identification technique had a variance accounted for (VAF) of less than 75%. Representations using the first and second Volterra kernels had a much higher VAF (90-97%) as well as a lower Akaike information criteria (AICc) indicating that the Volterra kernel models were more efficient. The experimental second Volterra kernel matches well with results from a dynamic-parameter nonlinearity model with fixed mass as a function of depth as well as stiffness and damping that increase with depth into the skin. A study with 16 subjects showed that the kernel peak values have mean coefficients of variation (CV) that ranged from 3 to 8% and showed that the kernel principal components were correlated with location on the body, subject mass, body mass index (BMI), and gender. These fast and robust methods for Volterra kernel stochastic system identification can be applied to the characterization of biological tissues, diagnosis of skin diseases, and determination of consumer product efficacy.
Algebraic Integrability of Lotka-Volterra equations in three dimensions
Constandinides, Kyriacos
2009-01-01
We examine the algebraic complete integrability of Lotka-Volterra equations in three dimensions. We restrict our attention to Lotka-Volterra systems defined by a skew symmetric matrix. We obtain a complete classification of such systems. The classification is obtained using Painleve analysis and more specifically by the use of Kowalevski exponents. The imposition of certain integrality conditions on the Kowalevski exponents gives necessary conditions for the algebraic integrability of the corresponding systems. We also show that the conditions are sufficient.
Lotka-Volterra representation of general nonlinear systems.
Hernández-Bermejo, B; Fairén, V
1997-02-01
In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.
Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM
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Reza Abazari
2013-01-01
Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.
On Modelling of Nonlinear Systems and Phenomena with the Use of Volterra and Wiener Series
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Andrzej Borys
2015-03-01
Full Text Available This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener kernels and operators. Also, the problem of a best approximation of large-scale nonlinear systems using Volterra operators in weighted Fock spaces is described. Examples of applications considered are the following: Volterra series use in description of nonlinear distortions in satellite systems and their equalization or compensation, exploiting Wiener kernels to modelling of biological systems, the use of both Volterra and Wiener theories in description of ocean waves and in magnetic resonance spectroscopy. Moreover, connections between Volterra series and neural network models, and also input-output descriptions of quantum systems by Volterra series are discussed. Finally, we consider application of Volterra series to solving some nonlinear problems occurring in hydrology, navigation, and transportation.
Kashani, Mahsa H.; Ghorbani, Mohammad Ali; Dinpashoh, Yagob; Shahmorad, Sedaghat
2016-09-01
Rainfall-runoff simulation is an important task in water resources management. In this study, an integrated Volterra model with artificial neural networks (IVANN) was presented to simulate the rainfall-runoff process. The proposed integrated model includes the semi-distributed forms of the Volterra and ANN models which can explore spatial variation in rainfall-runoff process without requiring physical characteristic parameters of the catchments, while taking advantage of the potential of Volterra and ANNs models in nonlinear mapping. The IVANN model was developed using hourly rainfall and runoff data pertaining to thirteen storms to study short-term responses of a forest catchment in northern Iran; and its performance was compared with that of semi-distributed integrated ANN (IANN) model and lumped Volterra model. The Volterra model was applied as a nonlinear model (second-order Volterra (SOV) model) and solved using the ordinary least square (OLS) method. The models performance were evaluated and compared using five performance criteria namely coefficient of efficiency, root mean square error, error of total volume, relative error of peak discharge and error of time for peak to arrive. Results showed that the IVANN model performs well than the other semi-distributed and lumped models to simulate the rainfall-runoff process. Comparing to the integrated models, the lumped SOV model has lower precision to simulate the rainfall-runoff process.
Nonstandard numerical integrations of a Lotka-Volterra system
Bhowmik, S.K.
2009-01-01
In this article, we consider a three dimensional Lotka-Volterra system. We have developed some nonstandard numerical integrations of the model which preserve all properties of real solutions, and they are consistent. We have shown some numerical results to support this methods.
Integrability of Lotka-Volterra Planar Complex Cubic Systems
Dukarić, Maša; Giné, Jaume
In this paper, we study the Lotka-Volterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, except one which remains open, using different methods.
Nonstandard numerical integrations of a Lotka-Volterra system
Bhowmik, S.K.
2009-01-01
In this article, we consider a three dimensional Lotka-Volterra system. We have developed some nonstandard numerical integrations of the model which preserve all properties of real solutions, and they are consistent. We have shown some numerical results to support this methods.
Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW
Zhu, Li; Fan, Qibin
2013-05-01
Fractional calculus is an extension of derivatives and integrals to non-integer orders and has been widely used to model scientific and engineering problems. In this paper, we describe the fractional derivative in the Caputo sense and give the second kind Chebyshev wavelet (SCW) operational matrix of fractional integration. Then based on above results we propose the SCW operational matrix method to solve a kind of nonlinear fractional-order Volterra integro-differential equations. The main characteristic of this approach is that it reduces the integro-differential equations into a nonlinear system of algebraic equations. Thus, it can simplify the problem of fractional order equation solving. The obtained numerical results indicate that the proposed method is efficient and accurate for this kind equations.
Calculation of Volterra kernels for solutions of nonlinear differential equations
van Hemmen, JL; Kistler, WM; Thomas, EGF
2000-01-01
We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of
Calculation of Volterra kernels for solutions of nonlinear differential equations
van Hemmen, JL; Kistler, WM; Thomas, EGF
2000-01-01
We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of th
Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces
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Rigoberto Medina
2016-01-01
Full Text Available We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated.
Lotka-Volterra type equations and their explicit integration
Gervais, Jean-Loup; Jean-Loup Gervais; Mikhail V Saveliev
1994-01-01
In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar A_n case, possessing a representation without branching. This allows us, in particular, to treat the first fundamental representations of A_r, B_r, C_r, and G_2 on the same footing.
Backward stochastic Volterra integral equations- a brief survey
Institute of Scientific and Technical Information of China (English)
YONG Jiong-min
2013-01-01
In this paper, we present a brief survey on the updated theory of backward stochas-tic Volterra integral equations (BSVIEs, for short). BSVIEs are a natural generalization of backward stochastic diff erential equations (BSDEs, for short). Some interesting motivations of studying BSVIEs are recalled. With proper solution concepts, it is possible to establish the corresponding well-posedness for BSVIEs. We also survey various comparison theorems for solutions to BSVIEs.
Institute of Scientific and Technical Information of China (English)
鲁世平
2003-01-01
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second-order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second- order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
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Omar Abu Arqub
2012-01-01
Full Text Available This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ( is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ( is obtained and it is proved to converge to the exact solution (. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.
Numerical Integration and Synchronization for the 3-Dimensional Metriplectic Volterra System
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Gheorghe Ivan
2011-01-01
Full Text Available The main purpose of this paper is to study the metriplectic system associated to 3-dimensional Volterra model. For this system we investigate the stability problem and numerical integration via Kahan's integrator. Finally, the synchronization problem for two coupled metriplectic Volterra systems is discussed.
New homotopy analysis transform algorithm to solve volterra integral equation
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Sunil Kumar
2014-03-01
Full Text Available The main aim of the present work is to propose a new and simple algorithm for Volterra integral equation arising in demography, the study of viscoelastic materials, and in insurance mathematics through the renewal equation by using homotopy analysis transform method. The homotopy analysis transform method is an innovative adjustment in Laplace transform algorithm and makes the calculation much simpler. The solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. The beauty of the paper is coupling of two techniques. Finally, two numerical examples are given to show the accuracy and stability of this method.
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Berenguer MI
2010-01-01
Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .
Periodic solutions of Volterra integral equations
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M. N. Islam
1988-01-01
Full Text Available Consider the system of equationsx(t=f(t+∫−∞tk(t,sx(sds, (1andx(t=f(t+∫−∞tk(t,sg(s,x(sds. (2Existence of continuous periodic solutions of (1 is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1 it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1 and (2 are btained using the contraction mapping principle as the basic tool.
Nonlinear System Identification via Basis Functions Based Time Domain Volterra Model
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Yazid Edwar
2014-07-01
Full Text Available This paper proposes basis functions based time domain Volterra model for nonlinear system identification. The Volterra kernels are expanded by using complex exponential basis functions and estimated via genetic algorithm (GA. The accuracy and practicability of the proposed method are then assessed experimentally from a scaled 1:100 model of a prototype truss spar platform. Identification results in time and frequency domain are presented and coherent functions are performed to check the quality of the identification results. It is shown that results between experimental data and proposed method are in good agreement.
Linear Volterra Integral Equations as the Limit of Discrete Systems
Institute of Scientific and Technical Information of China (English)
M. Federson; R.Bianconi; L.Barbanti
2004-01-01
We consider the multidimensional abstract linear integral equation of Volterra typex (t)+(*)∫Rt a (s)x (s)ds =f (t),t∈R,as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions.The functions x,a and f are Banach space-valued de .ned on a compact interval R of R n ,R t is a subinterval of R depending on t∈R and (*)∫denotes either the Bochner-Lebesgue integral or the Henstock integral.The results presented here generalize those in [1]and are in the spirit of [3].As a consequence of our approach,it is possible to study the properties of (1)by transferring the properties of the discrete systems.The Henstock integral setting enables us to consider highly oscillating functions.
Nonlinear features identified by Volterra series for damage detection in a buckled beam
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Shiki S. B.
2014-01-01
Full Text Available The present paper proposes a new index for damage detection based on nonlinear features extracted from prediction errors computed by multiple convolutions using the discrete-time Volterra series. A reference Volterra model is identified with data in the healthy condition and used for monitoring the system operating with linear or nonlinear behavior. When the system has some structural change, possibly associated with damage, the index metrics computed could give an alert to separate the linear and nonlinear contributions, besides provide a diagnostic about the structural state. To show the applicability of the method, an experimental test is performed using nonlinear vibration signals measured in a clamped buckled beam subject to different levels of force applied and with simulated damages through discontinuities inserted in the beam surface.
On various integrable discretizations of a general two-component Volterra system
Babalic, Corina N.; Carstea, A. S.
2013-04-01
We present two integrable discretizations of a general differential-difference bicomponent Volterra system. The results are obtained by discretizing directly the corresponding Hirota bilinear equations in two different ways. Multisoliton solutions are presented together with a new discrete form of Lotka-Volterra equation obtained by an alternative bilinearization.
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Institute of Scientific and Technical Information of China (English)
Yun Li; Hiroshi Kashiwagi
2005-01-01
Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.
Shayma Adil Murad; Hussein Jebrail Zekri; Samir Hadid
2011-01-01
We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
A novel nonlinear adaptive filter using a pipelined second-order Volterra recurrent neural network.
Zhao, Haiquan; Zhang, Jiashu
2009-12-01
To enhance the performance and overcome the heavy computational complexity of recurrent neural networks (RNN), a novel nonlinear adaptive filter based on a pipelined second-order Volterra recurrent neural network (PSOVRNN) is proposed in this paper. A modified real-time recurrent learning (RTRL) algorithm of the proposed filter is derived in much more detail. The PSOVRNN comprises of a number of simple small-scale second-order Volterra recurrent neural network (SOVRNN) modules. In contrast to the standard RNN, these modules of a PSOVRNN can be performed simultaneously in a pipelined parallelism fashion, which can lead to a significant improvement in its total computational efficiency. Moreover, since each module of the PSOVRNN is a SOVRNN in which nonlinearity is introduced by the recursive second-order Volterra (RSOV) expansion, its performance can be further improved. Computer simulations have demonstrated that the PSOVRNN performs better than the pipelined recurrent neural network (PRNN) and RNN for nonlinear colored signals prediction and nonlinear channel equalization. However, the superiority of the PSOVRNN over the PRNN is at the cost of increasing computational complexity due to the introduced nonlinear expansion of each module.
ON SPECTRAL METHODS FOR VOLTERRA INTEGRAL EQUATIONS AND THE CONVERGENCE ANALYSIS
Institute of Scientific and Technical Information of China (English)
Tao Tang; Xiang Xu; Jin Cheng
2008-01-01
The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is pro-posed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach (with theoretical justification) for the Volterra type equations.
Institute of Scientific and Technical Information of China (English)
Rui QI; Cheng-jian ZHANG; Yu-jie ZHANG
2012-01-01
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k,l)-algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained.
Directory of Open Access Journals (Sweden)
Behzad Ghanbari
2014-01-01
Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.
Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.
2017-03-01
Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
Energy Technology Data Exchange (ETDEWEB)
Itoh, Yoshiaki [Institute of Statistical Mathematics and the Graduate University for Advanced Studies, 4-6-7 Minami-Azabu Minatoku, Tokyo 106-8569 (Japan)], E-mail: itoh@ism.ac.jp
2009-01-16
The combinatorial method is useful to obtain conserved quantities for some nonlinear integrable systems, as an alternative to the Lax representation method. Here we extend the combinatorial method and introduce an elementary geometry to show the vanishing of the Poisson brackets of the Hamiltonian structure for a Lotka-Volterra system of competing species. We associate a set of points on a circle with a set of species of the Lotka-Volterra system, where the dominance relations between points are given by the dominance relations between the species. We associate each term of the conserved quantities with a subset of points on the circle, which simplifies to show the vanishing of the Poisson brackets.
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
DEFF Research Database (Denmark)
E. Barndorff-Nielsen, Ole; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G∗ of Potthoff--Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
Controllability of Urysohn integral inclusions of Volterra type
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Thomas S. Angell
2010-06-01
Full Text Available The aim of this paper is to study the controllability of a system described by an integral inclusion of Urysohn type with delay. In our approach we reduce the controllability problem of the nonlinear system into solvability problem of another integral inclusion. The solvability of this integral inclusion is subsequently established by imposing suitable standard boundedness, convexity and semicontinuity conditions on the set-valued mapping defining the integral inclusion, and by employing Bohnenblust-Karlin extension of Kakutani's fixed point theorem for set-valued mappings.
Institute of Scientific and Technical Information of China (English)
丁皓江; 王惠明; 陈伟球
2004-01-01
The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating.
Wang, Tianxiao
2010-01-01
This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present to illustrate the aforementioned optimal control problem. Motivated by the technical skills in solving above problem, a more convenient and briefer method for the unique solvability of M-solution for BSVIEs is proposed. At last, we will investigate a risk minimization problem by means of the maximum principle for FBSVIEs. Closed-form optimal portfolio is obtained in some special cases.
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Shayma Adil Murad
2011-01-01
Full Text Available We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
Energy Technology Data Exchange (ETDEWEB)
Manson, G; Worden, K, E-mail: graeme.manson@sheffield.ac.u, E-mail: k.worden@sheffield.ac.u [Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Mappin St, Sheffield S1 3JD (United Kingdom)
2009-08-01
Although a great deal of work has been carried out on structural dynamic systems under random excitation, there has been a comparatively small amount of this work concentrating on the calculation of the quantities commonly measured in structural dynamic tests. Among the existing work, the Volterra series, a means of predicting nonlinear system response for weakly nonlinear systems, has allowed the computation of various measurable quantities of interest for structural dynamics, including: auto- and cross-spectra, FRFs, coherences and higher-order spectra. These calculations are quite intensive and are typically only possible using computer algebra. A previous calculation by the authors for the coherence for a Duffing oscillator yielded results which showed some qualitatitive disagreement with numerical simulation; the object of the current paper is simply to extend the calculation in order to see if better agreement can be achieved.
Kvaternik, Raymond G.; Silva, Walter A.
2008-01-01
A computational procedure for identifying the state-space matrices corresponding to discrete bilinear representations of nonlinear systems is presented. A key feature of the method is the use of first- and second-order Volterra kernels (first- and second-order pulse responses) to characterize the system. The present method is based on an extension of a continuous-time bilinear system identification procedure given in a 1971 paper by Bruni, di Pillo, and Koch. The analytical and computational considerations that underlie the original procedure and its extension to the title problem are presented and described, pertinent numerical considerations associated with the process are discussed, and results obtained from the application of the method to a variety of nonlinear problems from the literature are presented. The results of these exploratory numerical studies are decidedly promising and provide sufficient credibility for further examination of the applicability of the method.
Al Jarro, Ahmed
2011-09-01
A new predictor-corrector scheme for solving the Volterra integral equation to analyze transient electromagnetic wave interactions with arbitrarily shaped inhomogeneous dielectric bodies is considered. Numerical results demonstrating stability and accuracy of the proposed method are presented. © 2011 IEEE.
Institute of Scientific and Technical Information of China (English)
Dishen; Jiabu
2006-01-01
This paper studies the stability and boundedness of the solutions of Volterra integral differential equations with infinite delay in the phase space (Ch, |·|h), the h-uniform stability, h-uniformly asymptotic stability and h-boundedness of solutions are obtained.
Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales
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Eleonora Messina
2015-01-01
Full Text Available We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.
Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
Damianou, P. A.; Evripidou, C. A.; Kassotakis, P.; Vanhaecke, P.
2017-03-01
Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in a special case when A is a Toeplitz matrix where all off-diagonal entries are plus or minus one. In this case, the associated Lotka-Volterra system turns out to be a reduction of Liouville integrable systems, whose integrability was shown by Bogoyavlenskij and Itoh. We prove that the reduced systems are also Liouville integrable and that they are also non-commutative integrable by constructing a set of independent first integrals, having the required involutive properties (with respect to the Poisson bracket). These first integrals fall into two categories. One set consists of polynomial functions that are restriction of the Bogoyavlenskij-Itoh integrals; their involutivity was already pointed out by Bogoyavlenskij. The other set consists of rational functions which are obtained through a Poisson map from the first integrals of some recently discovered superintegrable Lotka-Volterra systems. The fact that these polynomial and rational first integrals, combined, have the required properties for Liouville and non-commutative integrability is quite remarkable; the quite technical proof of functional independence of the first integrals is given in detail.
Systems of nonlinear Volterra integro-differential equations of arbitrary order
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Kourosh Parand
2018-10-01
Full Text Available In this paper, a new approximate method for solving of systems of nonlinear Volterra integro-differential equations of arbitrary (integer and fractional order is introduced. For this purpose, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs based on the classical Chebyshev polynomials of the first kind has been introduced that can be used to obtain the solution of the integro-differential equations (IDEs. Also, we construct the fractional derivative operational matrix of order $\\alpha$ in the Caputo's definition for GFCFs. This method reduced a system of IDEs by collocation method into a system of algebraic equations. Some examples to illustrate the simplicity and the effectiveness of the propose method have been presented.
Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind
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Abdon Atangana
2013-01-01
Full Text Available This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.
Hybrid function method for solving Fredholm and Volterra integral equations of the second kind
Hsiao, Chun-Hui
2009-08-01
Numerical solutions of Fredholm and Volterra integral equations of the second kind via hybrid functions, are proposed in this paper. Based upon some useful properties of hybrid functions, integration of the cross product, a special product matrix and a related coefficient matrix with optimal order, are applied to solve these integral equations. The main characteristic of this technique is to convert an integral equation into an algebraic; hence, the solution procedures are either reduced or simplified accordingly. The advantages of hybrid functions are that the values of n and m are adjustable as well as being able to yield more accurate numerical solutions than the piecewise constant orthogonal function, for the solutions of integral equations. We propose that the available optimal values of n and m can minimize the relative errors of the numerical solutions. The high accuracy and the wide applicability of the hybrid function approach will be demonstrated with numerical examples. The hybrid function method is superior to other piecewise constant orthogonal functions [W.F. Blyth, R.L. May, P. Widyaningsih, Volterra integral equations solved in Fredholm form using Walsh functions, Anziam J. 45 (E) (2004) C269-C282; M.H. Reihani, Z. Abadi, Rationalized Haar functions method for solving Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200 (2007) 12-20] for these problems.
Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems
Aziz, Waleed
2011-01-01
We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizability are obtained for (1,-1,1), (2,-1,1) and (1,-2,1)-resonance. To prove sufficiency, we mainly use the method of Darboux with extensions for inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable.
On the polynomial first integrals of the ({ital a},{ital b},{ital c}) Lotka{endash}Volterra system
Energy Technology Data Exchange (ETDEWEB)
Labrunie, S. [Service de physique de l`etat condense, Centre d`etudes de Saclay, 91191 Gif sur Yvette (France)
1996-11-01
Using elementary differential algebraic techniques, we prove that the 3D Lotka{endash}Volterra dynamical system has no other nontrivial polynomial first integrals than the previously known ones. {copyright} {ital 1996 American Institute of Physics.}
Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels
2012-01-01
Existence of extremal solutions of nonlinear discontinuous integral equations of Volterra type is proved. This result is extended herein to functional Volterra integral equations (FVIEs) and to a system of discontinuous VIEs as well.
Directory of Open Access Journals (Sweden)
shadan sadigh behzadi
2012-03-01
Full Text Available In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i Modified Adomian decomposition method (MADM, (ii Variational iteration method (VIM, (iii Homotopy analysis method (HAM and (iv Modified homotopy perturbation method (MHPM. The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.
Evolutionary Network Control also holds for nonlinear networks: Ruling the Lotka-Volterra model
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Alessandro Ferrarini
2015-09-01
Full Text Available The proof of our understanding of ecological and biological systems is measured by our skill to rule them, i.e. to channelize them towards a desired state. Control is a cardinal issue in most complex systems, but because a general theory to apply it in a quantitative manner has been absent so far, little was known about how we can rule weighted, directed networks that represent the most common configuration of real systems. To this purpose, Evolutionary Network Control (ENC has been developed as a theoretical and methodological framework aimed to the control of ecological and biological networks by coupling network dynamics and evolutionary modelling. ENC is a tools to address controllability for arbitrary network topologies and sizes. ENC has proven to cover several topics of network control, e.g. a the global control from inside and b from outside, c the local (step-by-step control, and the computation of: d control success, e feasibility, and f degree of uncertainty. Taken together, these results indicate that many aspects of controllability can be explored exactly and analytically for arbitrary networks, opening new avenues to deepening our understanding of complex systems. As yet, I have applied ENC only to linear ecological and biological networks. In this work, I show that ENC also holds for any kind of nonlinear networks, and provide an applicative example based on the nonlinear, widely-used, Lotka-Volterra model.
Ritzberger, D.; Jakubek, S.
2017-09-01
In this work, a data-driven identification method, based on polynomial nonlinear autoregressive models with exogenous inputs (NARX) and the Volterra series, is proposed to describe the dynamic and nonlinear voltage and current characteristics of polymer electrolyte membrane fuel cells (PEMFCs). The structure selection and parameter estimation of the NARX model is performed on broad-band voltage/current data. By transforming the time-domain NARX model into a Volterra series representation using the harmonic probing algorithm, a frequency-domain description of the linear and nonlinear dynamics is obtained. With the Volterra kernels corresponding to different operating conditions, information from existing diagnostic tools in the frequency domain such as electrochemical impedance spectroscopy (EIS) and total harmonic distortion analysis (THDA) are effectively combined. Additionally, the time-domain NARX model can be utilized for fault detection by evaluating the difference between measured and simulated output. To increase the fault detectability, an optimization problem is introduced which maximizes this output residual to obtain proper excitation frequencies. As a possible extension it is shown, that by optimizing the periodic signal shape itself that the fault detectability is further increased.
Shakurov, I R; Asadullin, R M
2014-01-01
In this article we study the inverse problem of finding coefficients of Lotka-Volterra's equations on one given solution. The conditions of the uniqueness and existence of the inverse problem are found.
A predictor-corrector scheme for solving the Volterra integral equation
Al Jarro, Ahmed
2011-08-01
The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been developed for removing low and high frequency instabilities. On the other hand, literature on stabilizing explicit schemes, which might be considered more efficient since they do not require a matrix inversion at each time step, is practically non-existent. In this work, a stable but still explicit predictor-corrector scheme is proposed for solving the Volterra integral equation and its efficacy is verified numerically. © 2011 IEEE.
Equivalent HPM with ADM and Convergence of the HPM to a Class of Nonlinear Integral Equations
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J. Manafian Heris
2013-03-01
Full Text Available The purpose of this study is to implement homotopy perturbation method, for solving nonlinear Volterra integral equations. In this work, a reliable approach for convergence of the HPM when applied to a class of nonlinear Volterra integral equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The results obtained by using HPM, are compared to those obtained by using Adomian decomposition method alone. The numerical results, demonstrate that HPM technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM
Nonlinear Imaging of Microbubble Contrast Agent Using the Volterra Filter: In Vivo Results.
Du, Juan; Liu, Dalong; Ebbini, Emad S
2016-12-01
A nonlinear filtering approach to imaging the dynamics of microbubble ultrasound contrast agents (UCAs) in microvessels is presented. The approach is based on the adaptive third-order Volterra filter (TVF), which separates the linear, quadratic, and cubic components from beamformed pulse-echo ultrasound data. The TVF captures polynomial nonlinearities utilizing the full spectral components of the echo data and not from prespecified bands, e.g., second or third harmonics. This allows for imaging using broadband pulse transmission to preserve the axial resolution and the SNR. In this paper, we present the results from imaging the UCA activity in a 200- [Formula: see text] cellulose tube embedded in a tissue-mimicking phantom using a linear array diagnostic probe. The contrast enhancement was quantified by computing the contrast-to-tissue ratio (CTR) for the different imaging components, i.e., B-mode, pulse inversion (PI), and the TVF components. The temporal mean and standard deviation of the CTR values were computed for all frames in a given data set. Quadratic and cubic images, referred to as QB-mode and CB-mode, produced higher mean CTR values than B-mode, which showed improved sensitivity. Compared with PI, they produced similar or higher mean CTR values with greater spatial specificity. We also report in vivo results from imaging UCA activity in an implanted LNCaP tumor with heterogeneous perfusion. The temporal means and standard deviations of the echogenicity were evaluated in small regions with different perfusion levels in the presence and absence of UCA. The in vivo measurements behaved consistently with the corresponding calculations obtained under microflow conditions in vitro. Specifically, the nonlinear VF components produced larger increases in the temporal mean and standard deviation values compared with B-mode in regions with low to relatively high perfusion. These results showed that polynomial filters such as the TVF can provide an important tool
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
An algebraic structure of discrete zero curvature equations is established for integrable coupling systems associated with semi-direct sums of Lie algebras. As an application example of this algebraic structure, a τ-symmetry algebra for the Volterra lattice integrable couplings is engendered from this theory.
Energy Technology Data Exchange (ETDEWEB)
Lee, C.E.
1976-08-01
The Volterra method of the multiplicative integral is used to determine the isotopic density, mass, and energy production in linear systems. The solution method, assumptions, and limitations are discussed. The method allows a rapid accurate calculation of the change in isotopic density, mass, and energy production independent of the magnitude of the time steps, production or decay rates, or flux levels.
Imai, Kenji
2014-02-01
In this paper, a new n-dimensional homogeneous Lotka-Volterra (HLV) equation, which possesses a Lie symmetry, is derived by the extension from a three-dimensional HLV equation. Its integrability is shown from the viewpoint of Lie symmetries. Furthermore, we derive dynamical systems of higher order, which possess the Lie symmetry, using the algebraic structure of this HLV equation.
Energy Technology Data Exchange (ETDEWEB)
Cairo, Laurent [MAPMO/CNRS-Departement de Mathematiques, Universite d' Orleans, 45067 Orleans, Cedex 2 (France); Llibre, Jaume [Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain)
2007-06-15
We classify all the global phase portraits of the cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2. For such vector fields there are exactly 28 different global phase portraits in the Poincare disc up to a reversal of sense of all orbits.
Analog integrated circuits for the Lotka-Volterra competitive neural networks.
Asai, T; Ohtani, M; Yonezu, H
1999-01-01
A subthreshold MOS integrated circuit (IC) is designed and fabricated for implementing a competitive neural network of the Lotka-Volterra (LV) type which is derived from conventional membrane dynamics of neurons and is used for the selection of external inputs. The steady-state solutions to the LV equation can be classified into three types, each of which represents qualitatively different selection behavior. Among the solutions, the winners-share-all (WSA) solution in which a certain number of neurons remain activated in steady states is particularly useful owing to robustness in the selection of inputs from a noisy environment. The measured results of the fabricated LV IC's agree well with the theoretical prediction as long as the influence of device mismatches is small. Furthermore, results of extensive circuit simulations prove that the large-scale LV circuit producing the WSA solution does exhibit a reliable selection compared with winner-take-all circuits, in the possible presence of device mismatches.
Numerical treatments for solving nonlinear mixed integral equation
Directory of Open Access Journals (Sweden)
M.A. Abdou
2016-12-01
Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2014-06-01
Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.
Volterra integrodifferential systems
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K. Balachandran
1995-01-01
Full Text Available Sufficient conditions for the complete controllability of nonlinear perturbations of Volterra integrodifferential systems with implicit derivative are established. The results generalize the results of Dauer and Balachandran [9] and are obtained through the notions of condensing map and measure of noncompactness of a set.
Institute of Scientific and Technical Information of China (English)
Shu-hua Zhang; Tao Lin; Yan-ping Lin; Ming Rao
2001-01-01
In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initialvalue problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of aposteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
Wilson, Alan
2008-08-01
It is shown that Boltzmann's methods from statistical physics can be applied to a much wider range of systems, and in a variety of disciplines, than has been commonly recognized. A similar argument can be applied to the ecological models of Lotka and Volterra. Furthermore, it is shown that the two methodologies can be applied in combination to generate the Boltzmann, Lotka and Volterra (BLV) models. These techniques enable both spatial interaction and spatial structural evolution to be modelled, and it is argued that they potentially provide a much richer modelling methodology than that currently used in the analysis of 'scale-free' networks.
On generalized Volterra systems
Charalambides, S. A.; Damianou, P. A.; Evripidou, C. A.
2015-01-01
We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The algorithm uses the root system of a complex simple Lie algebra. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka-Volterra system. We present in detail all such systems in the cases of A3, A4 and we also give some examples from higher dimensions. We classify all possible Lotka-Volterra systems that arise via this algorithm in the An case.
Exponential Observers for Lotka-Volterra Systems
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Dr. V. Sundarapandian
2011-03-01
Full Text Available This paper solves the exponential observer design problem for Lotka-Volterra systems. Explicitly, Sundarapandian’s theorem (2002 for observer design for exponential observer design is used to solve the nonlinear observer design problem for 2-species, 3-species and 4-species Lotka-Volterra systems. Numerical examples are provided to illustrate the effectiveness of the proposed exponential observer design for the Lotka-Volterra systems.
Nonclassical linear Volterra equations of the first kind
Apartsyn, Anatoly S
2003-01-01
This monograph deals with linear integra Volterra equations of the first kind with variable upper and lower limits of integration. Volterra operators of this type are the basic operators for integral models of dynamic systems.
Institute of Scientific and Technical Information of China (English)
DING Hao-jiang; WANG Hui-ming
2005-01-01
The elastodynamic problems of magneto-electro-elastic hollow cylinders in the state ofaxisymmetric plane strain case can be transformed into two Volterra integral equations of the second kind about two functions with respect to time. Interpolation functions were introduced to approximate two unknown functions in each time subinterval and two new recursive formulae are derived. By using the recursive formulae, numerical results were obtained step by step. Under the same time step, the accuracy of the numerical results by the present method is much higher than that by the traditional quadrature method.
Al Jarro, Ahmed
2011-08-01
A hybrid MPI/OpenMP scheme for efficiently parallelizing the explicit marching-on-in-time (MOT)-based solution of the time-domain volume (Volterra) integral equation (TD-VIE) is presented. The proposed scheme equally distributes tested field values and operations pertinent to the computation of tested fields among the nodes using the MPI standard; while the source field values are stored in all nodes. Within each node, OpenMP standard is used to further accelerate the computation of the tested fields. Numerical results demonstrate that the proposed parallelization scheme scales well for problems involving three million or more spatial discretization elements. © 2011 IEEE.
Romano, Alessandro
This article is a first application of an integrable nonautonomous Lotka-Volterra (LV) model to the study of tourism dynamics. In particular, we analyze the interaction in terms of touristic flows among three Italian regions. Confirming an hypothesis advanced by recent theoretical works, we find that these regions not only compete against each other, but at times they also proceed in mutualism. Moreover, the kind and the intensity of the interaction changes over time, suggesting that dynamic models can play a vital role in the study of touristic flows.
Romano, Alessandro
2016-01-01
This article is a first application of an integrable nonautonomous Lotka–Volterra (LV) model to the study of tourism dynamics. In particular, we analyze the interaction in terms of touristic flows among three Italian regions. Confirming an hypothesis advanced by recent theoretical works, we find that these regions not only compete against each other, but at times they also proceed in mutualism. Moreover, the kind and the intensity of the interaction changes over time, suggesting that dynamic models can play a vital role in the study of touristic flows. PMID:27661615
DEFF Research Database (Denmark)
Chon, K H; Holstein-Rathlou, N H; Marsh, D J
1998-01-01
via the Laguerre expansion technique achieve this prediction NMSE with approximately half the number of free parameters relative to either neural-network model. However, both approaches are deemed effective in modeling nonlinear dynamic systems and their cooperative use is recommended in general....
Volterra Series Based Distortion Effect
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2010-01-01
A large part of the characteristic sound of the electric guitar comes from nonlinearities in the signal path. Such nonlinearities may come from the input- or output-stage of the amplier, which is often equipped with vacuum tubes or a dedicated distortion pedal. In this paper the Volterra series e...
Sidorov, Denis
2012-01-01
Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic approximation of the parametric family of generalized solutions is constructed. The method for the solution's regular part refinement is proposed using the successive approximations method.
Directory of Open Access Journals (Sweden)
Ni Hua
2012-01-01
Full Text Available With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. The main results improve and generalize the former corresponding results.
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
THE PARALLEL RECURSIVE AP ADAPTIVE ALGORITHM BASED ON VOLTERRA SERIES
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Aiming at the nonlinear system identification problem, a parallel recursive affine projection (AP) adaptive algorithm for the nonlinear system based on Volterra series is presented in this paper. The algorithm identifies in parallel the Volterra kernel of each order, recursively estimate the inverse of the autocorrelation matrix for the Volterra input of each order, and remarkably improve the convergence speed of the identification process compared with the NLMS and conventional AP adaptive algorithm based on Volterra series. Simulation results indicate that the proposed method in this paper is efficient.
Solving Volterra's Population Model Using New Second Derivative Multistep Methods
Directory of Open Access Journals (Sweden)
K. Parand
2008-01-01
Full Text Available In this study new second derivative multistep methods (denoted SDMM are used to solve Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential where the integral term represents the effect of toxin. This model is first converted to a nonlinear ordinary differential equation and then the new SDMM, which has good stability and accuracy properties, are applied to solve this equation. We compare this method with the others and show that new SDMM gives excellent results.
Nonlinear Young integrals via fractional calculus
Hu, Yaozhong (1961-); Le, Khoa
2015-01-01
For H\\"older continuous functions $W(t,x)$ and $\\varphi_t$, we define nonlinear integral $\\int_a^b W(dt, \\varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.
Lotka-Volterra system with Volterra multiplier.
Gürlebeck, Klaus; Ji, Xinhua
2011-01-01
With the aid of Volterra multiplier, we study ecological equations for both tree system and cycle system. We obtain a set of sufficient conditions for the ultimate boundedness to nonautonomous n-dimensional Lotka-Volterra tree systems with continuous time delay. The criteria are applicable to cooperative model, competition model, and predator-prey model. As to cycle system, we consider a three-dimensional predator-prey Lotka-Volterra system. In order to get a condition under which the system is globally asymptotic stable, we obtain a Volterra multiplier, so that in a parameter region the system is with the Volterra multiplier it is globally stable. We have also proved that in regions in which the condition is not satisfied, the system is unstable or at least it is not globally stable. Therefore, we say that the three-dimensional cycle system is with global bifurcation.
An integrable symmetric (2+1)-dimensional Lotka-Volterra equation and a family of its solutions
Energy Technology Data Exchange (ETDEWEB)
Hu Xingbiao [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Li Chunxia [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Nimmo, Jonathan J C [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China)
2005-01-07
A symmetric (2+1)-dimensional Lotka-Volterra equation is proposed. By means of a dependent variable transformation, the equation is firstly transformed into multilinear form and further decoupled into bilinear form by introducing auxiliary independent variables. A bilinear Baecklund transformation is found and then the corresponding Lax pair is derived. Explicit solutions expressed in terms of pfaffian solutions of the bilinear form of the symmetric (2+1)-dimensional Lotka-Volterra equation are given. As a special case of the pfaffian solutions, we obtain soliton solutions and dromions.
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed
Jing, Xingjian
2015-01-01
This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain. The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis a...
Institute of Scientific and Technical Information of China (English)
Emiko ISHIWATA; Yoshiaki MUROYA
2009-01-01
To compute long term integrations for the pantograph differential equation with proportional delay qt,0 ＜ q ≤1:y'(t) = ay(t) + by(qt) +f(t),y(0) = Yo,we offer two kinds of numerical methods using special mesh distributions,that is,a rational approximant with 'quasi-uniform meshes'(see E.Ishiwata and Y.Muroya [Appl.Math.Comput.,2007,187:741-747]) and a Gauss collocation method with 'quasi-constrained meshes'.If we apply these meshes to rational approximant and Gauss collocation method,respectively,then we obtain useful numerical methods of order p* = 2m for computing long term integrations. Numerical investigations for these methods are also presented.
Zhao, Peng; Fan, Engui
2015-04-01
In this paper, a new type of integrable differential-difference hierarchy, namely, the generalized relativistic Lotka-Volterra (GRLV) hierarchy, is introduced. This hierarchy is closely related to Lotka-Volterra lattice and relativistic Lotka-Volterra lattice, which allows us to provide a unified and effective way to obtain some exact solutions for both the Lotka-Volterra hierarchy and the relativistic Lotka-Volterra hierarchy. In particular, we shall construct algebro-geometric quasiperiodic solutions for the LV hierarchy and the RLV hierarchy in a unified manner on the basis of the finite gap integration theory.
Directory of Open Access Journals (Sweden)
Chang Tan
2013-01-01
Full Text Available By piecewise Euler method, a discrete Lotka-Volterra predator-prey model with impulsive effect at fixed moment is proposed and investigated. By using Floquets theorem, we show that a globally asymptotically stable pest-eradication periodic solution exists when the impulsive period is less than some critical value. Further, we prove that the discrete system is permanence if the impulsive period is larger than some critical value. Finally, some numerical experiments are given.
Directory of Open Access Journals (Sweden)
Masato Shinjo
2015-12-01
Full Text Available The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka–Volterra (dhLV system, which is an integrable variant of the famous prey–predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant.
Nonlinear structural analysis using integrated force method
Indian Academy of Sciences (India)
N R B Krishnam Raju; J Nagabhushanam
2000-08-01
Though the use of the integrated force method for linear investigations is well-recognised, no efforts were made to extend this method to nonlinear structural analysis. This paper presents the attempts to use this method for analysing nonlinear structures. General formulation of nonlinear structural analysis is given. Typically highly nonlinear bench-mark problems are considered. The characteristic matrices of the elements used in these problems are developed and later these structures are analysed. The results of the analysis are compared with the results of the displacement method. It has been demonstrated that the integrated force method is equally viable and efficient as compared to the displacement method.
Librescu, Liviu
2001-01-01
Within this NASA Grant, the following points should be emphasized: 1) All the objectives stated in the proposal of the grant have been accomplished. Moreover. the activity within the project has addressed additional issues, of the linear and nonlinear aeroelasticity, not included in the objectives of the grant. 2) During the activities within the grant, we have been in a permanent contact with Dr. Walter A. Silva, the monitor of the NASA Project, to whom we have reported continuously our achievements. 3) As a result of the activities within the grant a number of papers: a. have been submitted for publication to the AIAA Journals, namely the AIAA Journal and the Journal of Guidance, Control, and Dynamics, and b. have been presented at the specialized National Conferences and an International Congress, and have appeared in the proceedings of these Conferences. 4) A list of papers submitted for publication and presented at Conferences is appended herewith. 5) In all these papers, an acknowledgment to NASA Langley Research Center was included.
Study on Volterra-Laguerre behavioral model for RF power amplifier
Institute of Scientific and Technical Information of China (English)
Nan Jingchang; Liu Yuanan; Tang Bihua
2007-01-01
Volterra series behavioral model for radio frequency(RF)power amplifier(PA)has been widely used in system-level simulation,however,high computational complexity makes this kind of model limited to"weak"nonlinearity.In order to reduce the computational complexity and the number of coefficients of Volterra series kernels,a Volterra series improved behavioral model based on Lasuerre orthogonal polynomials function,namely Volterra-Laguerre behavioral model,is proposed.Mathematical expressions of Volterra-Laguerre behavioral model is derived.and accuracy of the model is verified through comparison of measured and simulation output data from a freescale PA using MRF21030 transistor.Mathematical analysis and simulation results show that Volterra-Laguerre behavioral model has a simple structure,much less coefficients and better modeling performance than general Volterra series model.The model can be used more correctly for system-level simulation of RF PA with wideband signal.
Optimal control of stochastic difference Volterra equations an introduction
Shaikhet, Leonid
2015-01-01
This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equation...
Completely integrable models of nonlinear optics
Indian Academy of Sciences (India)
Andrey I Maimistov
2001-11-01
The models of the nonlinear optics in which solitons appeared are considered. These models are of paramount importance in studies of nonlinear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency and parametric interaction of three waves. At present there are a number of theories based on completely integrable systems of equations, which are, both, generations of the original known models and new ones. The modiﬁed Korteweg-de Vries equation, the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation, Sine–Gordon equation, the reduced Maxwell–Bloch equation, Hirota equation, the principal chiral ﬁeld equations, and the equations of massive Thirring model are some soliton equations, which are usually to be found in nonlinear optics theory.
On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model
Directory of Open Access Journals (Sweden)
Attila Dénes
2016-09-01
Full Text Available We make more realistic our model [Nonlinear Anal. 73(2010, 650-659] on the coexistence of fishes and plants in Lake Tanganyika. The new model is an asymptotically autonomous system whose limiting equation is a Lotka-Volterra system. We give conditions for the phenomenon that the trajectory of any solution of the original non-autonomous system "rolls up"' onto a cycle of the limiting Lotka-Volterra equation as $t\\to\\infty$, which means that the limit set of the solution of the non-autonomous system coincides with the cycle. A counterexample is constructed showing that the key integral condition on the coefficient function in the original non-autonomous model cannot be dropped. Computer simulations illustrate the results.
High resolution 3D nonlinear integrated inversion
Institute of Scientific and Technical Information of China (English)
Li Yong; Wang Xuben; Li Zhirong; Li Qiong; Li Zhengwen
2009-01-01
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
Some Nonlinear Integral Inequalities on Time Scales
Directory of Open Access Journals (Sweden)
Li Wei Nian
2007-01-01
Full Text Available The purpose of this paper is to investigate some nonlinear integral inequalities on time scales. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. The theoretical results are illustrated by a simple example at the end of this paper.
Generalized Bihari Type Integral Inequalities and the Corresponding Integral Equations
2009-01-01
We study some special nonlinear integral inequalities and the corresponding integral equations in measure spaces. They are significant generalizations of Bihari type integral inequalities and Volterra and Fredholm type integral equations. The kernels of the integral operators are determined by concave functions. Explicit upper bounds are given for the solutions of the integral inequalities. The integral equations are investigated with regard to the existence of a minimal and a maximal soluti...
Nonlinear Physics Integrability, Chaos and Beyond
Lakshmanan, M
1997-01-01
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramatically raising our perception of many natural phenomena, these concepts are opening up new vistas of applications and unfolding technologies: Optical soliton based information technology, magnetoelectronics, controlling and synchronization of chaos and secure communications, to name a few. These developments have raised further new interesting questions and potentialities. We present a particular view of some of the challenging problems and payoffs ahead in the next few decades by tracing the early historical events, summarizing the revolutionary era of 1950-70 when many important new ideas including solitons and chaos were ...
Volterra, Fascism, and France.
Capristo, Annalisa
2015-12-01
My contribution focuses on two aspects strictly related each other. On one hand, the progressive marginalization of Volterra from Italian scientific and political life after the rise of Fascism - because of his public anti-Fascist stance, both as a senator and as a professor - until his definitive exclusion on racial grounds in 1938. On the other hand, the reactions of his French colleagues and friends to this ostracism, and the support he received from them. As it emerges from several sources (Volterra's correspondence, institutional documentation, conference proceedings, etc.), it was mainly thanks to their support that he was able to escape the complete isolation and the "civil death" to which the regime condemned many of its adversaries.
Splitting methods for partial Volterra integro-differential equations
Brunner, H.; Houwen, P.J. van der; Sommeijer, B.P.
1999-01-01
The spatial discretization of initial-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multiste
Some stability conditions for scalar Volterra difference equations
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2016-01-01
Full Text Available New explicit stability results are obtained for the following scalar linear difference equation \\[x(n+1-x(n=-a(nx(n+\\sum_{k=1}^n A(n,kx(k+f(n\\] and for some nonlinear Volterra difference equations.
Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy
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Xiuzhi Xing
2014-01-01
Full Text Available Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.
New Method for Identifying Finite Degree Volterra Series
Suleiman, Wael; Monin, André
2008-01-01
International audience; In this paper, the identification of a class of nonlinear systems which admits input-output maps described by a finite degree Volterra series is considered. In actual fact, it appears that this class can model many important nonlinear multivariable processes not only in engineering, but also in biology, socio-economics, and ecology. To solve this identification problem, we propose a method based on a local gradient search in a local parameterization of the state space ...
Nonlinear Dynamics: Integrability, Chaos and Patterns
Energy Technology Data Exchange (ETDEWEB)
Grammaticos, B [GMPIB, Universite Paris VII, Tour 24--14, 5e etage, Case 7021, 75251 Paris (France)
2004-02-06
When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like 'verify the relation 14.81'. Others are less so, such as 'prepare a write-up on a) frequency
Nonlinear Equalization of Microwave Photonic Links
2016-10-31
3[1…3] = [1][2][3] the Volterra model reduces to the Taylor series. TABLE I VOLTERRA KERNEL COEFFICIENTS FOR...ORDER 3 M UNIQUE VOLTERRA COEFFICIENTS 8 120 16 816 64 45760 128 357760 256 2829056 The main benefit of a Volterra model over a Taylor ...nonlinear equalizer works on the entire Nyquist band and is synthesized directly from mathematical requirements instead of using best - fit methods
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Institute of Scientific and Technical Information of China (English)
邢维; 田华
2014-01-01
We considered the polynomial first integral for reversible Lotka-Volterra model which describes the oscillatory chemical dynamics in a closed isothermal reaction.Making use of integrability theories of semi-quasihomogeneous systems,we proved that the Lotka-Votterra model is a unique polynomial first integral.%考虑一类描述闭等温反应中振荡化学动力学行为的可逆 Lotka-Volterra模型的多项式首次积分，利用半拟齐次系统的可积性理论，找到 Lotka-Volterra模型的一个多项式首次积分，并证明了它是Lotka-Volterra模型唯一的多项式首次积分。
A Multiple Iterated Integral Inequality and Applications
Directory of Open Access Journals (Sweden)
Zongyi Hou
2014-01-01
Full Text Available We establish new multiple iterated Volterra-Fredholm type integral inequalities, where the composite function w(u(s of the unknown function u with nonlinear function w in integral functions in [Ma, QH, Pečarić, J: Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities. Nonlinear Anal. 69 (2008 393–407] is changed into the composite functions w1(u(s,w2(u(s,…, wn (u(s of the unknown function u with different nonlinear functions w1,w2,…,wn, respectively. By adopting novel analysis techniques, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.
A Cauchy problem in nonlinear heat conduction
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy); Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli, 1, 06123 Perugia (Italy); Sanchini, G [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy)
2006-06-09
A Cauchy problem on the semiline for a nonlinear diffusion equation is considered, with a boundary condition corresponding to a prescribed thermal conductivity at the origin. The problem is mapped into a moving boundary problem for the linear heat equation with a Robin-type boundary condition. Such a problem is then reduced to a linear integral Volterra equation of II type which admits a unique solution.
Turing patterns in a modified Lotka-Volterra model
Energy Technology Data Exchange (ETDEWEB)
McGehee, Edward A. [Department of Chemistry, Williams College, Williamstown, MA 01267 (United States); Peacock-Lopez, Enrique [Department of Chemistry, Williams College, Williamstown, MA 01267 (United States)]. E-mail: epeacock@williams.edu
2005-07-04
In this Letter we consider a modified Lotka-Volterra model widely known as the Bazykin model, which is the MacArthur-Rosenzweig (MR) model that includes a prey-dependent response function and is modified with the inclusion of intraspecies interactions. We show that a quadratic intra-prey interaction term, which is the most realistic nonlinearity, yields sufficient conditions for Turing patterns. For the Bazykin model we find the Turing region in parameter space and Turing patterns in one dimension.
Bounds for solutions to retarded nonlinear double integral inequalities
Directory of Open Access Journals (Sweden)
Sabir Hussain
2014-12-01
Full Text Available We present bounds for the solution to three types retarded nonlinear integral inequalities in two variables. By doing this, we generalizing the results presented in [3,12]. To illustrate our results, we present some applications.
Global satisfactory control for nonlinear integrator processes with long delay
Institute of Scientific and Technical Information of China (English)
Yiqun YANG; Guobo XIANG
2007-01-01
Integrator processes with long delay are difficult to control. Nonlinear characteristics of actuators make the control problem more challenging. A technique is proposed in this paper for global satisfactory control (GSC) of such processes with relay-type nonlinearity. An oscillatory control signal is injected into the nonlinear process; the amplitude and frequency of the oscillatory signal are designed to linearise the nonlinear process in the sense of harmonic analysis; and a state feedback controller is configured to implement GSC over the linearised process. An illustrative example is given to demonstrate the effectiveness of the proposed method.
Large nonlinear w$_{\\infty}$ algebras from nonlinear integrable deformations of self dual gravity
Castro, C
1994-01-01
A proposal for constructing a universal nonlinear {\\hat W}_{\\infty} algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of D=4 Self Dual Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket based on nonlinear gauge theories associated with infinite dimensional Lie algebras. A Quantization and supersymmetrization program can also be carried out. The relevance to the Kadomtsev-Petviashvili hierarchy, 2D dilaton gravity, quantum gravity and black hole physics is discussed in the concluding remarks.
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.
2009-10-01
Geometric ideas are present in many areas of modern theoretical physics and they are usually associated with the presence of nonlinear phenomena. Integrable nonlinear systems play a prime role both in geometry itself and in nonlinear physics. One can mention general relativity, exact solutions of the Einstein equations, string theory, Yang-Mills theory, instantons, solitons in nonlinear optics and hydrodynamics, vortex dynamics, solvable models of statistical physics, deformation quantization, and many others. Soliton theory now forms a beautiful part of mathematics with very strong physical motivations and numerous applications. Interactions between mathematics and physics associated with integrability issues are very fruitful and stimulating. For instance, spectral theories of linear quantum mechanics turned out to be crucial for studying nonlinear integrable systems. The modern theory of integrable nonlinear partial differential and difference equations, or the `theory of solitons', is deeply rooted in the achievements of outstanding geometers of the end of the 19th and the beginning of the 20th century, such as Luigi Bianchi (1856-1928) and Jean Gaston Darboux (1842-1917). Transformations of surfaces and explicit constructions developed by `old' geometers were often rediscovered or reinterpreted in a modern framework. The great progress of recent years in so-called discrete geometry is certainly due to strong integrable motivations. A very remarkable feature of the results of the classical integrable geometry is the quite natural (although nontrivial) possibility of their discretization. This special issue is dedicated to Jean Gaston Darboux and his pioneering role in the development of the geometric ideas of modern soliton theory. The most famous aspects of his work are probably Darboux transformations and triply orthogonal systems of surfaces, whose role in modern mathematical physics cannot be overestimated. Indeed, Darboux transformations play a central
Täuber, Uwe C.
2013-03-01
Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka-Volterra model is characterized by neutral cycles in phase space, describing undamped oscillations for both predator and prey populations. In contrast, Monte Carlo simulations for stochastic two-species predator-prey reaction systems on regular lattices display complex spatio-temporal structures associated with persistent erratic population oscillations. The Doi-Peliti path integral representation of the master equation for stochastic particle interaction models is utilized to arrive at a field theory action for spatial Lotka-Volterra models in the continuum limit. In the species coexistence phase, a perturbation expansion with respect to the nonlinear predation rate is employed to demonstrate that spatial degrees of freedom and stochastic noise induce instabilities toward structure formation, and to compute the fluctuation corrections for the oscillation frequency and diffusion coefficient. The drastic downward renormalization of the frequency and the enhanced diffusivity are in excellent qualitative agreement with Monte Carlo simulation data.
Nonlinear Integrated Optical Waveguides in Chalcogenide Glasses
Institute of Scientific and Technical Information of China (English)
Yinlan; Ruan; Barry; Luther-Davies; Weitang; Li; Andrei; Rode; Marek; Samoc
2003-01-01
This paper reports on the study and measurement of the third order optical nonlinearity in bulk sulfide-based chalcogenide glasses; The fabrication process of the ultrafast laser deposited As-S-(Se)-based chalcogenide films and optical waveguides using two techniques: wet chemistry etching and plasma etching.
Darboux polynomials for Lotka-Volterra systems in three dimensions
Christodoulides, Yiannis T
2008-01-01
We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.
Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation
Kekatos, Vassilis
2011-01-01
Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. ...
Nonlinear dynamics non-integrable systems and chaotic dynamics
Borisov, Alexander
2017-01-01
This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.
Nonlinear Integral Sliding Mode Control for a Second Order Nonlinear System
Directory of Open Access Journals (Sweden)
Xie Zheng
2015-01-01
Full Text Available A nonlinear integral sliding-mode control (NISMC scheme is proposed for second order nonlinear systems. The new control scheme is characterized by a nonlinear integral sliding manifold which inherits the desired properties of the integral sliding manifold, such as robustness to system external disturbance. In particular, compared with four kinds of sliding mode control (SMC, the proposed control scheme is able to provide better transient performances. Furthermore, the proposed scheme ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance is proved by Lyapunov stability theory and LaSalle invariance principle. Finally, both the theoretical analysis and simulation examples demonstrate the validity of the proposed scheme.
Institute of Scientific and Technical Information of China (English)
倪华; 田立新; 张平正
2011-01-01
With the help of a substitution and applying the fixed point theorem, we derive a criterion of the existence of positive almost periodic solutions for a class of Lotka-Volterra type system.The main results improve and generalize the former results.%通过变换和不动点定理,研究了一类非线性Lotka-Volterra系统的正概周期解的存在性,获得了新的结果.
A Simple Transfer Function for Nonlinear Dendritic Integration
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Matt eSingh
2015-08-01
Full Text Available Relatively recent advances in patch clamp recordings and iontophoresis have enabled unprecedented study of neuronal post-synaptic integration (dendritic integration. Findings support a separate layer of integration in the dendritic branches before potentials reach the cell’s soma. While integration between branches obeys previous linear assumptions, proximal inputs within a branch produce threshold nonlinearity, which some authors have likened to the sigmoid function. Here we show the implausibility of a sigmoidal relation and present a more realistic transfer function in both an elegant artificial form and a biophysically derived form that further considers input locations along the dendritic arbor. As the distance between input locations determines their ability to produce nonlinear interactions, models incorporating dendritic topology are essential to understanding the computational power afforded by these early stages of integration. We use the biophysical transfer function to emulate empirical data using biophysical parameters and describe the conditions under which the artificial and biophysically derived forms are equivalent.
Platforms for integrated nonlinear optics compatible with silicon integrated circuits
Moss, David J
2014-01-01
Nonlinear photonic chips are capable of generating and processing signals all-optically with performance far superior to that possible electronically - particularly with respect to speed. Although silicon has been the leading platform for nonlinear optics, its high two-photon absorption at telecommunications wavelengths poses a fundamental limitation. We review recent progress in CMOS-compatible platforms for nonlinear optics, focusing on Hydex glass and silicon nitride and briefly discuss the promising new platform of amorphous silicon. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation, ultrafast optical pulse generation and measurement. We highlight their potential future impact as well as the challenges to achieving practical solutions for many key applications.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
The Volterra series as special case of artificial neural network model
Napiorkowski, J.; O Kane, J. P.
2003-04-01
The geophysical processes contributing to the hydrological cycle are described by theoretically sound non-linear partial differential equations of mass and energy transfer. The hydrodynamic equations describing hydrological processes were developed in non-linear form in the nineteenth century. In the case of surface runoff from a natural catchment or flow in an open channel, an accurate application of the hydraulic approach requires a detailed topographical survey and determination of roughness parameters. In order to avoid these difficulties, alternative approaches e.g. via conceptual models and black box models were developed in the second half of the last century. The conceptual model approach is to simulate the nature of the catchment response or the channel response by relatively simple non-linear model built up from simple non-linear elements, e.g. cascade of non-linear reservoirs. Each non-linear reservoir is responsible for part of the attenuation of the system response. This lumped dynamic model can be represented by a set of ordinary differential equations: begin{gathered} dot S_1 (t) = - f[S_1 (t)] + x(t) dot S_2 (t) = - f[S_2 (t)] + f[S_1 (t)] ... dot S_n (t) = - f[S_n (t)] + f[Sn - 1 (t)] y(t) = f[S_n (t)] % MathType!End!2!1! (1) where x is the input signal(rainfall or flow at the upstream end of the channel), Si is the storage in the i-th reservoir, f(.) represents the outflow-storage relation and y is the output signal (surface runoff or flow at the downstream end of the channel). Non-linear black box analysis is concerned with representing a system by a functional Volterra series in the form of a sum of convolution integrals: begin{gathered} y(t) = intlimits_0^t {h_1 (τ )x(t - τ )dτ + intlimits_0^t {intlimits_0^t {h_2 (τ _1 ,τ _2 )x(t - τ _1 )x(t - τ _2 )dτ _1 dτ _2 } } } quad quad + intlimits_0^t {intlimits_0^t {intlimits_0^t {h_3 (τ _1 ,τ _2 ,τ _3 )x(t - τ _1 )x(t - τ _2 )x(t - τ _3 )dτ _1 dτ _2 dτ _3 } + ...} } % MathType!End!2
First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators
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R. Naz
2011-01-01
Full Text Available We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.
Photonic Integrated Devices for Nonlinear Optics
Caspani, Lucia; Dolgaleva, Ksenia; Wagner, Sean; Ferrera, Marcello; Razzari, Luca; Pasquazi, Alessia; Peccianti, Marco; Moss, David J; Aitchison, J Stewart; Morandotti, Roberto
2014-01-01
We review our recent progresses on frequency conversion in integrated devices, focusing primarily on experiments based on strip-loaded and quantum-well intermixed AlGaAs waveguides, and on CMOS-compatible high-index doped silica glass waveguides. The former includes both second- and third-order interactions, demonstrating wavelength conversion by tunable difference-frequency generation over a bandwidth of more than nm, as well as broadband self-phase modulation and tunable four-wave mixing. The latter includes four-wave mixing using low-power continuous-wave light in microring resonators as well as hyper-parametric oscillation in a high quality factor resonator, towards the realization of an integrated multiple wavelength source with important applications for telecommunications, spectroscopy, and metrology.
Accelerator-feasible N -body nonlinear integrable system
Danilov, V.; Nagaitsev, S.
2014-12-01
Nonlinear N -body integrable Hamiltonian systems, where N is an arbitrary number, have attracted the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
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Zhengduo Shan
2014-01-01
Full Text Available With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
Zhengduo Shan; Hongwei Yang; Baoshu Yin
2014-01-01
With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI) hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
Nonlinear partial differential equations: Integrability, geometry and related topics
Krasil'shchik, Joseph; Rubtsov, Volodya
2017-03-01
Geometry and Differential Equations became inextricably entwined during the last one hundred fifty years after S. Lie and F. Klein's fundamental insights. The two subjects go hand in hand and they mutually enrich each other, especially after the "Soliton Revolution" and the glorious streak of Symplectic and Poisson Geometry methods in the context of Integrability and Solvability problems for Non-linear Differential Equations.
Global Format for Conservative Time Integration in Nonlinear Dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc. generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with essentially nonlinear structures. These problems are overcome in...
Qualitative permanence of Lotka-Volterra equations.
Hofbauer, Josef; Kon, Ryusuke; Saito, Yasuhisa
2008-12-01
In this paper, we consider permanence of Lotka-Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka-Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence.
Experimental analysis of a Lotka-Volterra neural network for classification
Sukhu, Christopher L.; Stanton, Joseph; Aylesworth, Marc
2015-06-01
An experimental study of a neural network modeled by an adaptive Lotka-Volterra system follows. With totally inhibitory connections, this system can be embedded in a simple classification network. This network is able to classify and monitor its inputs in a spontaneous nonlinear fashion without prior training. We describe a framework for leveraging this behavior through an example involving breast cancer diagnosis.
Chromatic and Dispersive Effects in Nonlinear Integrable Optics
Webb, Stephen D; Valishev, Alexander; Nagaitsev, Sergei N; Danilov, Viatcheslav V
2015-01-01
Proton accumulator rings and other circular hadron accelerators are susceptible to intensity-driven parametric instabilities because the zero-current charged particle dynamics are characterized by a single tune. Landau damping can suppress these instabilities, which requires energy spread in the beam or introducing nonlinear magnets such as octupoles. However, this approach reduces dynamic aperture. Nonlinear integrable optics can suppress parametric instabilities independent of energy spread in the distribution, while preserving the dynamic aperture. This novel approach promises to reduce particle losses and enable order-of-magnitude increases in beam intensity. In this paper we present results, obtained using the Lie operator formalism, on how chromaticity and dispersion affect particle orbits in integrable optics. We conclude that chromaticity in general breaks the integrability, unless the vertical and horizontal chromaticities are equal. Because of this, the chromaticity correcting magnets can be weaker ...
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions
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Shoukry Ibrahim Atia El-Ganaini
2013-01-01
Full Text Available The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1-dimensional hyperbolic nonlinear Schrodinger (HNLS equation, the generalized nonlinear Schrodinger (GNLS equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.
Nonzero solutions of nonlinear integral equations modeling infectious disease
Energy Technology Data Exchange (ETDEWEB)
Williams, L.R. (Indiana Univ., South Bend); Leggett, R.W.
1982-01-01
Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, x(t) = ..integral../sup t//sub t-tau/f(s,x(s))ds, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if x(t) is the proportion of infectives at time t and f(t,x(t)) is the proportion of new infectives per unit time.
Directory of Open Access Journals (Sweden)
Fatima Sbeity
2013-01-01
Full Text Available Sub- and ultraharmonics generation by ultrasound contrast agents makes possible sub- and ultraharmonics imaging to enhance the contrast of ultrasound images and overcome the limitations of harmonic imaging. In order to separate different frequency components of ultrasound contrast agents signals, nonlinear models like single-input single-output (SISO Volterra model are used. One important limitation of this model is its incapacity to model sub- and ultraharmonic components. Many attempts are made to model sub- and ultraharmonics using Volterra model. It led to the design of mutiple-input singe-output (MISO Volterra model instead of SISO Volterra model. The key idea of MISO modeling was to decompose the input signal of the nonlinear system into periodic subsignals at the subharmonic frequency. In this paper, sub- and ultraharmonics modeling with MISO Volterra model is presented in a general framework that details and explains the required conditions to optimally model sub- and ultraharmonics. A new decomposition of the input signal in periodic orthogonal basis functions is presented. Results of application of different MISO Volterra methods to model simulated ultrasound contrast agents signals show its efficiency in sub- and ultraharmonics imaging.
Asymptotic solutions of forced nonlinear second order differential equations and their extensions
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Angelo B. Mingarelli
2007-03-01
Full Text Available Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented.
A mathematical model on fractional Lotka-Volterra equations.
Das, S; Gupta, P K
2011-05-21
The article presents the solutions of Lotka-Volterra equations of fractional-order time derivatives with the help of analytical method of nonlinear problem called the homotopy perturbation method (HPM). By using initial values, the explicit solutions of predator and prey populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The method performs extremely well in terms of efficiency and simplicity to solve this historical biological model. Copyright © 2011 Elsevier Ltd. All rights reserved.
Security analysis of chaotic communication systems based on Volterra-Wiener-Korenberg model
Energy Technology Data Exchange (ETDEWEB)
Lei Min [State Key Lab of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)] e-mail: leimin@sjtu.edu.cn; Meng Guang [State Key Lab of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China); Feng Zhengjin [Institute of Mechatronic Control System, Shanghai Jiao Tong University, Shanghai 200030 (China)
2006-04-01
Pseudo-randomicity is an important cryptological characteristic for proof of encryption algorithms. This paper proposes a nonlinear detecting method based on Volterra-Wiener-Korenberg model and suggests an autocorrelation function to analyze the pseudo-randomicity of chaotic secure systems under different sampling interval. The results show that: (1) the increase of the order of the chaotic transmitter will not necessarily result in a high degree of security; (2) chaotic secure systems have higher and stronger pseudo-randomicity at sparse sampling interval due to the similarity of chaotic time series to the noise; (3) Volterra-Wiener-Korenberg method can also give a further appropriate sparse sampling interval for improving the security of chaotic secure communication systems. For unmasking chaotic communication systems, the Volterra-Wiener-Korenberg technique can be applied to analyze the chaotic time series with surrogate data.
Adomian solution of a nonlinear quadratic integral equation
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E.A.A. Ziada
2013-04-01
Full Text Available We are concerned here with a nonlinear quadratic integral equation (QIE. The existence of a unique solution will be proved. Convergence analysis of Adomian decomposition method (ADM applied to these type of equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of Adomian’s series solution. Two methods are used to solve these type of equations; ADM and repeated trapezoidal method. The obtained results are compared.
B-Theory of Runge-Kutta methods for stiff Volterra functional differential equations
Institute of Scientific and Technical Information of China (English)
LI; Shoufu(李寿佛)
2003-01-01
B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differentialequations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs ofother type which appear in practice.
Excited state nonlinear integral equations for an integrable anisotropic spin-1 chain
Energy Technology Data Exchange (ETDEWEB)
Suzuki, J [Department of Physics, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka (Japan)
2004-12-17
We propose a set of nonlinear integral equations to describe the excited states of an integrable the spin-1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study of the supersymmetric sine-Gordon model.
Institute of Scientific and Technical Information of China (English)
Hermann BRUNNER
2009-01-01
The aims of this paper are (i) to present a survey of recent advances in the analysis of superconvergence of collocation solutions for linear Volterra-type functional integral and integro-differential equations with delay functions θ(t) vanishing at the initial point of the interval of integration (with θ(t) = qt (0 ＜ q ＜ 1,t ≥0) being an important special case),and (ii) to point,by means of a list of open problems,to areas in the numerical analysis of such Volterra functional equations where more research needs to be carried out.
A Biological Least-Action Principle for the Ecological Model of Volterra-Lotka
Samuelson, Paul A.
1974-01-01
The conservative model of Volterra for more-than-two predator-prey species is shown to be generated as extremals that minimize a definable Lagrange-Hamilton integral involving half the species and their rates of change. This least-action formulation differs from that derived two generations ago by Volterra, since his involves twice the number of phase variables and it employs as variables the cumulative integrals of the numbers of each species that have ever lived. The present result extends the variational, teleological formulations found a decade ago by the author to the more-than-two species case. The present result is anything but surprising, in view of the works by Kerner, Montroll, and others which apply Gibbs' statistical mechanics to the all-but-canonical equations of the standard Volterra model. By a globally linear transformation of coordinates, the Volterra equations are here converted into a completely canonical system isomorphic with the classical mechanics models of Newton, Lagrange, Hamilton, Jacobi, Boltzmann, Gibbs, Poincaré, and G. D. Birkhoff. The conservative nature of the Lotka-Volterra model, whatever its realism, is a crucially necessary condition for the applicability of the variational formalisms, microscopically and macroscopically. PMID:4528377
Two Kinds of Square-Conservative Integrators for Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
CHEN Jing-Bo; LIU Hong
2008-01-01
@@ Based on the Lie-group and Gauss-Legendre methods, two kinds of square-conservative integrators for squareconservative nonlinear evolution equations are presented. Lie-group based square-conservative integrators are linearly implicit, while Gauss-Legendre based square-conservative integrators are nonlinearly implicit and iterarive schemes are needed to solve the corresponding integrators. These two kinds of integrators provide natural candidates for simulating square-conservative nonlinear evolution equations in the sense that these integrators not only preserve the square-conservative properties of the continuous equations but also are nonlinearly stable.Numerical experiments are performed to test the presented integrators.
Directory of Open Access Journals (Sweden)
Xiao-Ping Chen
2016-01-01
Full Text Available The n-species Lotka-Volterra system with discrete delays is considered. The local asymptotic stability of positive equilibrium is investigated based on a contour integral method. The main purpose of this paper is to propose a new and general algorithm to study the local asymptotic stability of the positive equilibrium for the n-dimensional Lotka-Volterra system. Some numerical experiments are carried out to show the effectiveness of the proposed method.
Explicit Integration of Friedmann's Equation with Nonlinear Equations of State
Chen, Shouxin; Yang, Yisong
2015-01-01
This paper is a continuation of our earlier study on the integrability of the Friedmann equations in the light of the Chebyshev theorem. Our main focus will be on a series of important, yet not previously touched, problems when the equation of state for the perfect-fluid universe is nonlinear. These include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born--Infeld, and two-fluid models. We show that some of these may be integrated using Chebyshev's result while other are out of reach by the theorem but may be integrated explicitly by other methods. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution. For example, in the Chaplygin gas universe, it is seen that, as far as there is a tiny presence of nonlinear matter, linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics ...
Stability Criteria for Volterra Integrodynamic System
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Nusrat Yasmin
2015-01-01
Full Text Available We study conditions under which the solutions of linear Volterra integrodynamic system of the form yΔt=Atyt+∫t0tKt,sysΔs are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.
On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation
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Hameed Husam Hameed
2015-01-01
Full Text Available We develop the Newton-Kantorovich method to solve the system of 2×2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.
Laamiri, Imen; Khouaja, Anis; Messaoud, Hassani
2015-03-01
In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).
A nonlinear wave equation with a nonlinear integral equation involving the boundary value
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Thanh Long Nguyen
2004-09-01
Full Text Available We consider the initial-boundary value problem for the nonlinear wave equation $$displaylines{ u_{tt}-u_{xx}+f(u,u_{t}=0,quad xin Omega =(0,1,; 0
Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures
Institute of Scientific and Technical Information of China (English)
尤福财
2012-01-01
We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.
THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
王国灿; 金丽
2002-01-01
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained.The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
A simple nonlinear PD controller for integrating processes.
Dey, Chanchal; Mudi, Rajani K; Simhachalam, Dharmana
2014-01-01
Many industrial processes are found to be integrating in nature, for which widely used Ziegler-Nichols tuned PID controllers usually fail to provide satisfactory performance due to excessive overshoot with large settling time. Although, IMC (Internal Model Control) based PID controllers are capable to reduce the overshoot, but little improvement is found in the load disturbance response. Here, we propose an auto-tuning proportional-derivative controller (APD) where a nonlinear gain updating factor α continuously adjusts the proportional and derivative gains to achieve an overall improved performance during set point change as well as load disturbance. The value of α is obtained by a simple relation based on the instantaneous values of normalized error (eN) and change of error (ΔeN) of the controlled variable. Performance of the proposed nonlinear PD controller (APD) is tested and compared with other PD and PID tuning rules for pure integrating plus delay (IPD) and first-order integrating plus delay (FOIPD) processes. Effectiveness of the proposed scheme is verified on a laboratory scale servo position control system.
Lotka-Volterra systems satisfying a strong Painlevé property
Bountis, Tassos; Vanhaecke, Pol
2016-12-01
We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka-Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj , i ≠ j, and require that all variables diverge as t-1. We also require that the leading terms depend on n - 2 free parameters. We thus discover a cocycle relation among the coefficients aij of the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixi is added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.
Integrable nonlinear parity-time symmetric optical oscillator
Hassan, Absar U; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N
2016-01-01
The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain-thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time symmetric systems. Unlike other saturable parity time symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
Hierarchical Non-linear Image Registration Integrating Deformable Segmentation
Institute of Scientific and Technical Information of China (English)
RAN Xin; QI Fei-hu
2005-01-01
A hierarchical non-linear method for image registration was presented, which integrates image segmentation and registration under a variational framework. An improved deformable model is used to simultaneously segment and register feature from multiple images. The objects in the image pair are segmented by evolving a single contour and meanwhile the parameters of affine registration transformation are found out. After that, a contour-constrained elastic registration is applied to register the images correctly. The experimental results indicate that the proposed approach is effective to segment and register medical images.
Nonlinear Analysis and Intelligent Control of Integrated Vehicle Dynamics
Directory of Open Access Journals (Sweden)
C. Huang
2014-01-01
Full Text Available With increasing and more stringent requirements for advanced vehicle integration, including vehicle dynamics and control, traditional control and optimization strategies may not qualify for many applications. This is because, among other factors, they do not consider the nonlinear characteristics of practical systems. Moreover, the vehicle wheel model has some inadequacies regarding the sideslip angle, road adhesion coefficient, vertical load, and velocity. In this paper, an adaptive neural wheel network is introduced, and the interaction between the lateral and vertical dynamics of the vehicle is analyzed. By means of nonlinear analyses such as the use of a bifurcation diagram and the Lyapunov exponent, the vehicle is shown to exhibit complicated motions with increasing forward speed. Furthermore, electric power steering (EPS and active suspension system (ASS, which are based on intelligent control, are used to reduce the nonlinear effect, and a negotiation algorithm is designed to manage the interdependences and conflicts among handling stability, driving smoothness, and safety. Further, a rapid control prototype was built using the hardware-in-the-loop simulation platform dSPACE and used to conduct a real vehicle test. The results of the test were consistent with those of the simulation, thereby validating the proposed control.
A Fast Implicit Integration Scheme to Solve Highly Nonlinear System
Siddiquee, Saiful
Now-a-days researchers are formulating new generation of soil-models based on combined theory. That means researchers are trying to put forward a unified material model, which would predict at least the behaviour of all types of soils under all types of stress and time paths. So the solution techniques so far being used by the nonlinear Finite Element packages no longer can meet the huge demand of computational speed created by those models. It was necessary to develop a new type of solution scheme for the sophisticated models. Usually material nonlinearity makes it difficult to create a robust solution technique. So it is important to develop a solution scheme which will be very robust at the same time. That means the solution scheme should not break-down even for a notoriously complicated unified model. In this paper, we have developed an implicit solution scheme, which solves the resulting nonlinear equations of motion by implicit dynamic relaxation. There are a myriad number of implicit schemes for the use. Here a relatively less used method—called "Houbolt's integration scheme" has been used. It is very similar to the central difference scheme only difference is the use of the higher-order terms in the definition of velocity and acceleration. In order to make it faster, sparse-matrix solution scheme is used with partial pivoting and reordering of matrix elements to minimize the fill-ins. The combined effect is quite dramatic. It provides the main two traits of a good nonlinear solution technique—i.e., speed and robustness of solution. The solution scheme is applied to trace the full loading path of an elasto-visco-plastically defined material behaviour of a Plane Strain Compression (PSC) test sample. There is a huge gain in speed and robustness compared to the other techniques of solution.
Tang, Xianhua; Cao, Daomin; Zou, Xingfu
We consider a periodic Lotka-Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) x(t)=x(t)[r(t)-∑j=1na(t)x(t-τ(t))], i=1,2,…,n. We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright's 3/2 criteria for the autonomous delay logistic equation, and thereby, address the open problem proposed by both Kuang [Y. Kuang, Global stability in delayed nonautonomous Lotka-Volterra type systems without saturated equilibria, Differential Integral Equations 9 (1996) 557-567] and Teng [Z. Teng, Nonautonomous Lotka-Volterra systems with delays, J. Differential Equations 179 (2002) 538-561].
An existence theorem for Volterra integrodifferential equations with infinite delay
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Ferenc Izsak
2003-01-01
Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.
Generalized Lotka—Volterra systems connected with simple Lie algebras
Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A.
2015-06-01
We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a simple Lie algebra. We classify all subsets of the positive roots of the root system of type An for which the corresponding Hamiltonian systems are transformed, via a simple change of variables, to Lotka-Volterra systems. For some special cases of subsets of the positive roots of the root system of type An, we produce new integrable Hamiltonian systems.
On filtering over Îto-Volterra observations
Directory of Open Access Journals (Sweden)
Michael V. Basin
2000-01-01
Full Text Available In this paper, the Kalman-Bucy filter is designed for an Îto-Volterra process over Ito-Volterra observations that cannot be reduced to the case of a differential observation equation. The Kalman-Bucy filter is then designed for an Ito-Volterra process over discontinuous Ito-Volterra observations. Based on the obtained results, the filtering problem over discrete observations with delays is solved. Proofs of the theorems substantiating the filtering algorithms are given.
Sidorov, Denis
2011-01-01
The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing approximations of parametric families of solutions of such equations is suggested. The parametric family of solutions is constructed in terms of a logarithmic-power asymptotics.
Numerical solutions of stochastic Lotka-Volterra equations via operational matrices
Directory of Open Access Journals (Sweden)
F. Hosseini Shekarabi
2016-03-01
Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.
Quasipolynomial generalization of Lotka-Volterra mappings
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito; Brenig, Leon [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles, Campus Plaine - CP 231, Brussels (Belgium)]. E-mails: bhernand@ulb.ac.be; lbrenig@ulb.ac.be
2002-07-05
In recent years, it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as physics, population dynamics, chemistry and economy. The purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism (originally conceived for the analysis of ordinary differential equations) can be extended into the mapping domain. The extension of the formalism into the discrete-time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case. It will be demonstrated that Lotka-Volterra mappings play a central role in the quasipolynomial formalism for the discrete-time case. Moreover, the extension of the formalism into the discrete-time domain allows a significant generalization of Lotka-Volterra mappings as well as a whole transfer of algebraic methods into the discrete-time context. The result is a novel and more general conceptual framework for the understanding of Lotka-Volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of Lotka-Volterra mappings and their generalizations, but also for the development of new applications. (author)
Directory of Open Access Journals (Sweden)
A. Sami Bataineh
2008-01-01
Full Text Available The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM. The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.
A maximum principle for diffusive Lotka-Volterra systems of two competing species
Chen, Chiun-Chuan; Hung, Li-Chang
2016-10-01
Using an elementary approach, we establish a new maximum principle for the diffusive Lotka-Volterra system of two competing species, which involves pointwise estimates of an elliptic equation consisting of the second derivative of one function, the first derivative of another function, and a quadratic nonlinearity. This maximum principle gives a priori estimates for the total mass of the two species. Moreover, applying it to the system of three competing species leads to a nonexistence theorem of traveling wave solutions.
BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns
Grammaticos, B.
2004-02-01
When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like `verify the relation 14.81'. Others are less so, such as `prepare a write-up on a) frequency-locking and b) devil
Integrated optic devices based on nonlinear optical polymers
van Tomme, Emmanuel; van Daele, Peter P.; Baets, Roel G.; Lagasse, Paul E.
1991-03-01
An examination is made of the state of the art of nonlinear optical polymeric materials in view of their potential advantages. It is shown that these organic materials have many attractive features compared to LiNbO3 and III-V semiconductors with regard to their use in integrated optic circuits, especially since the level of integration is ever increasing. Considering more specifically electro-optic devices, a description is given of some of the theoretical background and basic properties. These polymers have already demonstrated a very high and extremely fast electro-optic effect compared to LiNbO3. It is also shown how low-loss waveguides can be fabricated by using easy techniques such as direct UV bleaching. The performance of phase modulators, Mach-Zehnder interferometers, and 2 x 2 space switches built with such polymers is already very promising. The results described in this study indicate a rapid rate of progress made by this technology, and one can expect that polymers in general and NLO polymers in particular will play an increasingly important role in integrated optics.
SINS/CNS Nonlinear Integrated Navigation Algorithm for Hypersonic Vehicle
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Yong-jun Yu
2015-01-01
Full Text Available Celestial Navigation System (CNS has characteristics of accurate orientation and strong autonomy and has been widely used in Hypersonic Vehicle. Since the CNS location and orientation mainly depend upon the inertial reference that contains errors caused by gyro drifts and other error factors, traditional Strap-down Inertial Navigation System (SINS/CNS positioning algorithm setting the position error between SINS and CNS as measurement is not effective. The model of altitude azimuth, platform error angles, and horizontal position is designed, and the SINS/CNS tightly integrated algorithm is designed, in which CNS altitude azimuth is set as measurement information. GPF (Gaussian particle filter is introduced to solve the problem of nonlinear filtering. The results of simulation show that the precision of SINS/CNS algorithm which reaches 130 m using three stars is improved effectively.
Nonlinear fusion for face recognition using fuzzy integral
Chen, Xuerong; Jing, Zhongliang; Xiao, Gang
2007-08-01
Face recognition based only on the visual spectrum is not accurate or robust enough to be used in uncontrolled environments. Recently, infrared (IR) imagery of human face is considered as a promising alternative to visible imagery due to its relative insensitive to illumination changes. However, IR has its own limitations. In order to fuse information from the two modalities to achieve better result, we propose a new fusion recognition scheme based on nonlinear decision fusion, using fuzzy integral to fuse the objective evidence supplied by each modality. The scheme also employs independent component analysis (ICA) for feature extraction and support vector machines (SVMs) for classification evidence. Recognition rate is used to evaluate the proposed scheme. Experimental results show the scheme improves recognition performance substantially.
Analytic treatment of nonlinear evolution equations using ﬁrst integral method
Indian Academy of Sciences (India)
Ahmet Bekir; Ömer Ünsal
2012-07-01
In this paper, we show the applicability of the ﬁrst integral method to combined KdV-mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations.
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen
2016-07-01
A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.
A NEW INTEGRAL INEQUALITY WITH POWER NONLINEARITY AND ITS DISCRETE ANALOGUE
Institute of Scientific and Technical Information of China (English)
杨恩浩
2001-01-01
A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.
Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2016-06-01
In this work, we establish a connection between the extended Prelle-Singer procedure and other widely used analytical methods to identify integrable systems in the case of nth-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods, we bring out the interlink between Lie point symmetries, contact symmetries, λ-symmetries, adjoint symmetries, null forms, Darboux polynomials, integrating factors, the Jacobi last multiplier and generalized λ-symmetries corresponding to the nth-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations.
Integral Terminal Sliding Mode Control for a Class of Nonaffine Nonlinear Systems with Uncertainty
Qiang Zhang; Hongliang Yu; Xiaohong Wang
2013-01-01
This paper is concerned with an integral terminal sliding mode tracking control for a class of uncertain nonaffine nonlinear systems. Firstly, the nonaffine nonlinear systems is approximated to facilitate the desired control design via a novel dynamic modeling technique. Next, for the unmeasured disturbance of nonlinear systems, integral terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to ...
Exactly conservation integrators
Energy Technology Data Exchange (ETDEWEB)
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J. [Univ. of Texas, Austin, TX (United States)
1999-03-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of any nonlinear invariants. In this work the authors present a general approach for developing explicit nontraditional algorithms that conserve such invariants exactly. They illustrate the method by applying it to the three-wave truncation of the Euler equations, the Lotka-Volterra predator-prey model, and the Kepler problem. The ideas are discussed in the context of symplectic (phase-space-conserving) integration methods as well as nonsymplectic conservative methods. They comment on the application of the method to general conservative systems.
Exactly conservative integrators
Energy Technology Data Exchange (ETDEWEB)
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1995-07-19
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves invariants. We illustrate the general method by applying it to the Three-Wave truncation of the Euler equations, the Volterra-Lotka predator-prey model, and the Kepler problem. We discuss our method in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Exactly conservative integrators
Shadwick, B A; Morrison, P J; Bowman, John C
1995-01-01
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Exactly conservative integrators
Energy Technology Data Exchange (ETDEWEB)
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1995-07-19
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves invariants. We illustrate the general method by applying it to the Three-Wave truncation of the Euler equations, the Volterra-Lotka predator-prey model, and the Kepler problem. We discuss our method in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Coupled Nonlinear Schr\\"{o}dinger equation and Toda equation (the Root of Integrability)
Hisakado, Masato
1997-01-01
We consider the relation between the discrete coupled nonlinear Schr\\"{o}dinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schr\\"{o}dinger equation. In the same way we can show the integrability in coupled case of dark and bright equations. Using this method we obtain several integrable equations.
A phenomenological Hamiltonian for the Lotka-Volterra problem
Energy Technology Data Exchange (ETDEWEB)
Georgian, T. [Corps of Engineers, Omaha, NE (United States); Findley, G.L. [Northeast Louisiana Univ., Monroe, LA (United States)
1996-12-31
We have presented a Hamiltonian theory of phenomenological chemical kinetics. In the present paper, we extend this treatment to the Lotka-Volterra model of sustained oscillations. Our approach begins with the usual definition of an intrinsic reaction coordinate space (x{sub 1},x{sub 2}) for the Lotka-Volterra problem, which leads to the rate equations x{sub 1}=ax{sub 1}-bx{sub 1}x{sub 2}, x{sub 2}=-cx{sub 2}+bx{sub 1}x{sub 2}, with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y{sub 1} = x{sub 1} and y{sub 2} = x{sub 2}] and an associated holonomic constraint, which give rise to the above rates as half of Hamilton`s equations. We provide trajectories by numerical integration (4th order Runge-Kutta) and show that H(x,y) is a constant of the motion. Finally, issues involved in developing an analytic solution to this problem are discussed.
Directory of Open Access Journals (Sweden)
Ammar Ali Neamah
2014-01-01
Full Text Available The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.
Nonlinear Bayesian cue integration explains the dynamics of vocal learning
Zhou, Baohua; Sober, Samuel; Nemenman, Ilya
The acoustics of vocal production in songbirds is tightly regulated during both development and adulthood as birds progressively refine their song using sensory feedback to match an acoustic target. Here, we perturb this sensory feedback using headphones to shift the pitch (fundamental frequency) of song. When the pitch is shifted upwards (downwards), birds eventually learn to compensate and sing lower (higher), bringing the experienced pitch closer to the target. Paradoxically, the speed and amplitude of this motor learning decrease with increases in the introduced error size, so that birds respond rapidly to a small sensory perturbation, while seemingly never correcting a much bigger one. Similar results are observed broadly across the animal kingdom, and they do not derive from a limited plasticity of the adult brain since birds can compensate for a large error as long as the error is imposed gradually. We develop a mathematical model based on nonlinear Bayesian integration of two sensory modalities (one perturbed and the other not) that quantitatively explains all of these observations. The model makes predictions about the structure of the probability distribution of the pitches sung by birds during the pitch shift experiments, which we confirm using experimental data. This work was supported in part by James S. McDonnell Foundation Grant # 220020321, NSF Grant # IOS/1208126, NSF Grant # IOS/1456912 and NIH Grants # R01NS084844.
Lie and conditional symmetries of the three-component diffusive Lotka-Volterra system
Cherniha, Roman; Davydovych, Vasyl'
2013-05-01
Lie and Q-conditional symmetries of the classical three-component diffusive Lotka-Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction-diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka-Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed.
Design automation for integrated nonlinear logic circuits (Conference Presentation)
Van Vaerenbergh, Thomas; Pelc, Jason; Santori, Charles; Bose, Ranojoy; Kielpinski, Dave; Beausoleil, Raymond G.
2016-05-01
A key enabler of the IT revolution of the late 20th century was the development of electronic design automation (EDA) tools allowing engineers to manage the complexity of electronic circuits with transistor counts now reaching into the billions. Recently, we have been developing large-scale nonlinear photonic integrated logic circuits for next generation all-optical information processing. At this time a sufficiently powerful EDA-style software tool chain to design this type of complex circuits does not yet exist. Here we describe a hierarchical approach to automating the design and validation of photonic integrated circuits, which can scale to several orders of magnitude higher complexity than the state of the art. Most photonic integrated circuits developed today consist of a small number of components, and only limited hierarchy. For example, a simple photonic transceiver may contain on the order of 10 building-block components, consisting of grating couplers for photonic I/O, modulators, and signal splitters/combiners. Because this is relatively easy to lay out by hand (or simple script) existing photonic design tools have relatively little automation in comparison to electronics tools. But demonstrating all-optical logic will require significantly more complex photonic circuits containing up to 1,000 components, hence becoming infeasible to design manually. Our design framework is based off Python-based software from Luceda Photonics which provides an environment to describe components, simulate their behavior, and export design files (GDS) to foundries for fabrication. At a fundamental level, a photonic component is described as a parametric cell (PCell) similarly to electronics design. PCells are described by geometric characteristics of their layout. A critical part of the design framework is the implementation of PCells as Python objects. PCell objects can then use inheritance to simplify design, and hierarchical designs can be made by creating composite
Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed
2016-08-01
In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.
Vibrations of Nonlinear Systems. The Method of Integral Equations,
Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not...parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to
On chaos in Lotka-Volterra systems: an analytical approach
Kozlov, Vladimir; Vakulenko, Sergey
2013-08-01
In this paper, we study Lotka-Volterra systems with N species and n resources. We show that the long time dynamics of these systems may be complicated. Depending on parameter choice, they can generate all types of hyperbolic dynamics, in particular, chaotic ones. Moreover, Lotka-Volterra systems can generate Lorenz dynamics. We state the conditions on the strong persistence of Lotka-Volterra systems when the number of resources is less than the number of species.
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)
2013-09-02
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.
Directory of Open Access Journals (Sweden)
Lakshmi Narayan Mishra
2016-04-01
Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.
On adjoint symmetry equations, integrating factors and solutions of nonlinear ODEs
Energy Technology Data Exchange (ETDEWEB)
Guha, Partha [Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig (Germany); Choudhury, A Ghose [Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta-700 009 (India); Khanra, Barun [Sailendra Sircar Vidyalaya, 62A Shyampukur Street, Calcutta-700 004 (India)], E-mail: partha.guha@mis.mpg.de, E-mail: a_ghosechoudhury@rediffmail.com, E-mail: barunkhanra@rediffmail.com
2009-03-20
We consider the role of the adjoint equation in determining explicit integrating factors and first integrals of nonlinear ODEs. In Chandrasekar et al (2006 J. Math. Phys. 47 023508), the authors have used an extended version of the Prelle-Singer method for a class of nonlinear ODEs of the oscillator type. In particular, we show that their method actually involves finding a solution of the adjoint symmetry equation. Next, we consider a coupled second-order nonlinear ODE system and derive the corresponding coupled adjoint equations. We illustrate how the coupled adjoint equations can be solved to arrive at a first integral.
Individual based modeling and parameter estimation for a Lotka-Volterra system.
Waniewski, J; Jedruch, W
1999-03-15
Stochastic component, inevitable in biological systems, makes problematic the estimation of the model parameters from a single sequence of measurements, despite the complete knowledge of the system. We studied the problem of parameter estimation using individual-based computer simulations of a 'Lotka-Volterra world'. Two kinds (species) of particles--X (preys) and Y (predators)--moved on a sphere according to deterministic rules and at the collision (interaction) of X and Y the particle X was changed to a new particle Y. Birth of preys and death of predators were simulated by addition of X and removal of Y, respectively, according to exponential probability distributions. With this arrangement of the system, the numbers of particles of each kind might be described by the Lotka-Volterra equations. The simulations of the system with low (200-400 particles on average) number of individuals showed unstable oscillations of the population size. In some simulation runs one of the species became extinct. Nevertheless, the oscillations had some generic properties (e.g. mean, in one simulation run, oscillation period, mean ratio of the amplitudes of the consecutive maxima of X and Y numbers, etc.) characteristic for the solutions of the Lotka-Volterra equations. This observation made it possible to estimate the four parameters of the Lotka-Volterra model with high accuracy and good precision. The estimation was performed using the integral form of the Lotka-Volterra equations and two parameter linear regression for each oscillation cycle separately. We conclude that in spite of the irregular time course of the number of individuals in each population due to stochastic intraspecies component, the generic features of the simulated system evolution can provide enough information for quantitative estimation of the system parameters.
Evolutionary stability in Lotka-Volterra systems.
Cressman, Ross; Garay, József
2003-05-21
The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem.
Integral and integrable algorithms for a nonlinear shallow-water wave equation
Camassa, Roberto; Huang, Jingfang; Lee, Long
2006-08-01
An asymptotic higher-order model of wave dynamics in shallow water is examined in a combined analytical and numerical study, with the aim of establishing robust and efficient numerical solution methods. Based on the Hamiltonian structure of the nonlinear equation, an algorithm corresponding to a completely integrable particle lattice is implemented first. Each "particle" in the particle method travels along a characteristic curve. The resulting system of nonlinear ordinary differential equations can have solutions that blow-up in finite time. We isolate the conditions for global existence and prove l1-norm convergence of the method in the limit of zero spatial step size and infinite particles. The numerical results show that this method captures the essence of the solution without using an overly large number of particles. A fast summation algorithm is introduced to evaluate the integrals of the particle method so that the computational cost is reduced from O( N2) to O( N), where N is the number of particles. The method possesses some analogies with point vortex methods for 2D Euler equations. In particular, near singular solutions exist and singularities are prevented from occurring in finite time by mechanisms akin to those in the evolution of vortex patches. The second method is based on integro-differential formulations of the equation. Two different algorithms are proposed, based on different ways of extracting the time derivative of the dependent variable by an appropriately defined inverse operator. The integro-differential formulations reduce the order of spatial derivatives, thereby relaxing the stability constraint and allowing large time steps in an explicit numerical scheme. In addition to the Cauchy problem on the infinite line, we include results on the study of the nonlinear equation posed in the quarter (space-time) plane. We discuss the minimum number of boundary conditions required for solution uniqueness and illustrate this with numerical
Similarity Reduction and Integrability for the Nonlinear Wave Equations from EPM Model
Institute of Scientific and Technical Information of China (English)
YAN ZhenYa
2001-01-01
Four types of similarity reductions are obtained for the nonlinear wave equation arising in the elasto-plasticmicrostructure model by using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou. As a result, the nonlinear wave equation is not integrable.``
Long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation
YAMANE, HIDESHI
2011-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation by means of the Deift-Zhou nonlinear steepest descent method. The leading term is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation
YAMANE, HIDESHI
2014-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation of Ablowitz-Ladik by means of the inverse scattering transform and the Deift-Zhou nonlinear steepest descent method. The leading part is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Travelling wave solutions to nonlinear physical models by means of the ﬁrst integral method
Indian Academy of Sciences (India)
İsmail Aslan Aslan
2011-04-01
This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully constructed for the equations considered.
Model uncertainty in economic impacts of climate change: Bernoulli versus Lotka Volterra dynamics.
Cooke, Roger M
2013-01-01
The dynamic economic behavior in most integrated assessment models linking economic growth to climate change involves a differential equation solved by Jacob Bernoulli in 1695. Using the dynamic integrated climate economy (DICE) model and freezing exogenous variables at initial values, this dynamic is shown to produce implausible projections on a 60-year time frame. If world capital started at US$1, after 60 years the world economy would be indistinguishable from one starting with 10 times the current capitalization. Such behavior points to uncertainty at the level of the fundamental dynamics, and suggests that discussions of discounting, utility, damage functions, and ethics should be conducted within a more general modeling vocabulary. Lotka Volterra dynamics is proposed as an alternative with greater prime facie plausibility. With near universality, economists assume that economic growth will go on forever. Lotka Volterra dynamics alert us to the possibility of collapse.
Brahim Tellab; Kamel Haouam
2016-01-01
In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.
MULTIPLE POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR HAMMERSTEIN TYPE INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Wang Feng; Zhang Fang; Liu Chunhan
2009-01-01
In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system is discussed.
Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions
Directory of Open Access Journals (Sweden)
Guotao Wang
2014-01-01
Full Text Available By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.
Directory of Open Access Journals (Sweden)
Sohrab Bazm
2016-02-01
Full Text Available In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficiency and accuracy of the method.
2011-01-01
International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a...
A new integrable discrete generalized nonlinear Schrodinger equation and its reductions
Li, Hongmin; Li, Yuqi; Chen, Yong
2013-01-01
A new integrable discrete system is constructed and studied, based on the algebraization of the difference operator. The model is named the discrete generalized nonlinear Schrodinger (GNLS) equation for which can be reduced to classical discrete nonlinear Schrodinger (NLS) equation. To show the complete integrability of the discrete GNLS equation, the recursion operator, symmetries and conservation quantities are obtained. Furthermore, all of reductions for the discrete GNLS equation are give...
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
Arino, O; Kimmel, M
1989-01-01
A model of cell cycle kinetics is proposed, which includes unequal division of cells, and a nonlinear dependence of the fraction of cells re-entering proliferation on the total number of cells in the cycle. The model is described by a nonlinear functional-integral equation. It is analyzed using the operator semigroup theory combined with classical differential equations approach. A complete description of the asymptotic behavior of the model is provided for a relatively broad class of nonlinearities. The nonnegative solutions either tend to a stable steady state, or to zero. The simplicity of the model makes it an interesting step in the analysis of dynamics of nonlinear structure populations.
Generalized Volterra lattices: Binary Darboux transformations and self-consistent sources
Müller-Hoissen, F.; Chvartatskyi, O.; Toda, K.
2017-03-01
We study two families of matrix versions of generalized Volterra (or Bogoyavlensky) lattice equations. For each family, the equations arise as reductions of a partial differential-difference equation in one continuous and two discrete variables, which is a realization of a general integrable equation in bidifferential calculus. This allows to derive a binary Darboux transformation and also self-consistent source extensions via general results of bidifferential calculus. Exact solutions are constructed from the simplest seed solutions.
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Reinhard Hochmuth
2002-01-01
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0＜σ＜∞ and (1+σ)-1＜τ＜∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
New CMOS Compatible Platforms for Integrated Nonlinear Optical Signal Processing
Moss, D J
2014-01-01
Nonlinear photonic chips have succeeded in generating and processing signals all-optically with performance far superior to that possible electronically - particularly with respect to speed. Although silicon-on-insulator has been the leading platform for nonlinear optics, its high two-photon absorption at telecommunications wavelengths poses a fundamental limitation. This paper reviews some of the recent achievements in CMOS-compatible platforms for nonlinear optics, focusing on amorphous silicon and Hydex glass, highlighting their potential future impact as well as the challenges to achieving practical solutions for many key applications. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation and ultrafast optical pulse generation and measurement.
On stochastic fractional Volterra equations in Hilbert space
Karczewska, Anna; Lizama, Carlos
2006-01-01
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition for a stochastic convolution to be a strong solution to a stochastic Volterra equation.
Time Reversal of Volterra Processes Driven Stochastic Differential Equations
Directory of Open Access Journals (Sweden)
L. Decreusefond
2013-01-01
Full Text Available We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past-dependent stochastic differential equations driven by a standard Brownian motion. We are then in position to derive existence and uniqueness of solutions of the Volterra driven SDE considered at the beginning.
Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures
Ferrera, M.; Razzari, L.; Duchesne, D.; Morandotti, R.; Yang, Z.; Liscidini, M.; Sipe, J. E.; Chu, S.; Little, B. E.; Moss, D. J.
2008-12-01
Photonic integrated circuits are a key component of future telecommunication networks, where demands for greater bandwidth, network flexibility, and low energy consumption and cost must all be met. The quest for all-optical components has naturally targeted materials with extremely large nonlinearity, including chalcogenide glasses and semiconductors, such as silicon and AlGaAs (ref. 4). However, issues such as immature fabrication technology for chalcogenide glass and high linear and nonlinear losses for semiconductors motivate the search for other materials. Here we present the first demonstration of nonlinear optics in integrated silica-based glass waveguides using continuous-wave light. We demonstrate four-wave mixing, with low (5 mW) continuous-wave pump power at λ = 1,550 nm, in high-index, doped silica glass ring resonators. The low loss, design flexibility and manufacturability of our device are important attributes for low-cost, high-performance, nonlinear all-optical photonic integrated circuits.
Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Technical Institute G. Cardano, Piazza della Resistenza 1, 00015 Monterotondo, Rome (Italy)
1997-08-01
Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}
Multi-Hamiltonian structure of Lotka-Volterra and quantum Volterra models
Energy Technology Data Exchange (ETDEWEB)
Cronstroem, C. [Nordisk Inst. for Teoretisk Fysik (NORDITA), Copenhagen (Denmark); Noga, M. [Department of Theoretical Physics, Comenius University, Mlynska Dolina, Bratislava (Slovakia)
1995-07-10
We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as a classical and as a quantum system. (orig.).
Multi-hamiltonian structure of Lotka-Volterra and quantum Volterra models
Cronström, C; Cronström, C; Noga, M
1994-01-01
We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as aclassical and as aquantal system
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter is gra...
Performance Analysis of Adaptive Volterra Filters in the Finite-Alphabet Input Case
Directory of Open Access Journals (Sweden)
Jaïdane Mériem
2004-01-01
Full Text Available This paper deals with the analysis of adaptive Volterra filters, driven by the LMS algorithm, in the finite-alphabet inputs case. A tailored approach for the input context is presented and used to analyze the behavior of this nonlinear adaptive filter. Complete and rigorous mean square analysis is provided without any constraining independence assumption. Exact transient and steady-state performances expressed in terms of critical step size, rate of transient decrease, optimal step size, excess mean square error in stationary mode, and tracking nonstationarities are deduced.
Optimal Parametric Iteration Method for Solving Multispecies Lotka-Volterra Equations
Directory of Open Access Journals (Sweden)
Vasile Marinca
2012-01-01
Full Text Available We apply an analytical method called the Optimal Parametric Iteration Method (OPIM to multispecies Lotka-Volterra equations. By using initial values, accurate explicit analytic solutions have been derived. The method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement has been demonstrated between the obtained solutions and the numerical ones. This new approach, which can be easily applied to other strongly nonlinear problems, is very effective and yields very accurate results.
Multistep epsilon-algorithm, Shanks' transformation, and Lotka-Volterra system by Hirota's method
Brezinski, Claude; Hu, Xing-Biao; Redivo-Zaglia, Michela; Sun, Jian-Qing
2010-01-01
In this paper, we give a multistep extension of the epsilon-algorithm of Wynn, and we show that it implements a multistep extension of the Shanks' sequence transformation which is defined by ratios of determinants. Reciprocally, the quantities defined in this transformation can be recursively computed by the multistep epsilon-algorithm. The multistep epsilon-algorithm and the multistep Shanks' transformation are related to an extended discrete Lotka-Volterra system. These results are obtained by using the Hirota's bilinear method, a procedure quite useful in the solution of nonlinear partial differential and difference equations.
NEW OSCILLATION CRITERIA RELATED TO EULER S INTEGRAL FOR CERTAIN NONLINEAR DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Using the integral average technique and a new function,some new oscillation criteria related to Euler integral are obtained for second order nonlinear differential equations with damping and forcing. Our results are of a higher degree of generality than some previous results. Information about the distribution of the zeros of solutions to the system is also obtained.
THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
N＇guimbi; Germain
2001-01-01
Abstract. The effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal Lz and H1 estimates for the error and its time derivative are established.
Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time
Institute of Scientific and Technical Information of China (English)
YAN Jun
2005-01-01
The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.
Permanence of Stochastic Lotka-Volterra Systems
Liu, Meng; Fan, Meng
2017-04-01
This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones. Then, we explore the permanence of two-dimensional stochastic Lotka-Volterra systems in a general setting, which models several different interactions between two species such as cooperation, competition, and predation. Sharp sufficient criteria are established with the help of the Lyapunov direct method and some new techniques. This study reveals that the stochastic noises play an essential role in the permanence and characterize the systems being permanent or not.
Energy Technology Data Exchange (ETDEWEB)
Stalin, S. [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India); Senthilvelan, M., E-mail: velan@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India)
2011-10-17
In this Letter, we formulate an exterior differential system for the newly discovered cubically nonlinear integrable Camassa-Holm type equation. From the exterior differential system we establish the integrability of this equation. We then study Cartan prolongation structure of this equation. We also discuss the method of identifying conservation laws and Baecklund transformation for this equation from the identified exterior differential system. -- Highlights: → An exterior differential system for a cubic nonlinear integrable equation is given. → The conservation laws from the exterior differential system is derived. → The Baecklund transformation from the Cartan-Ehresmann connection is obtained.
A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos
Institute of Scientific and Technical Information of China (English)
Yu Dong-Chuan; Wu Ai-Guo; Yang Chao-Ping
2005-01-01
A novel sliding mode nonlinear proportional-integral control (SMNPIC) scheme is proposed for driving a class of time-variant chaotic systems with uncertainty to arbitrarily desired trajectory with high accuracy. The SMNPIC differs from the previous sliding mode techniques in the sense that a nonlinear proportional-integral action of sliding function is involved in control law, so that both the steady-state error and the high-frequency chattering are reduced,and meanwhile, robustness and fastness are guaranteed. In addition, the proposed SMNPIC actually acts as a class of nonlinear proportional-integral-differential (PID) controller, in which the tracking error and its derivatives up to (n-1)thorder as well as the integral of tracking error are considered, so that more useful information than traditional PID can be implemented and better dynamic and static characteristics can obtained. Its good performance for chaotic control is illustrated through a During-Holmes system with uncertainty.
Integration of non-linear cellular mechanisms regulating microvascular perfusion.
Griffith, T M; Edwards, D H
1999-01-01
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
Filtered-X Affine Projection Algorithms for Active Noise Control Using Volterra Filters
Directory of Open Access Journals (Sweden)
Sicuranza Giovanni L
2004-01-01
Full Text Available We consider the use of adaptive Volterra filters, implemented in the form of multichannel filter banks, as nonlinear active noise controllers. In particular, we discuss the derivation of filtered-X affine projection algorithms for homogeneous quadratic filters. According to the multichannel approach, it is then easy to pass from these algorithms to those of a generic Volterra filter. It is shown in the paper that the AP technique offers better convergence and tracking capabilities than the classical LMS and NLMS algorithms usually applied in nonlinear active noise controllers, with a limited complexity increase. This paper extends in two ways the content of a previous contribution published in Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP '03, Grado, Italy, June 2003. First of all, a general adaptation algorithm valid for any order of affine projections is presented. Secondly, a more complete set of experiments is reported. In particular, the effects of using multichannel filter banks with a reduced number of channels are investigated and relevant results are shown.
Nonlinearity and fractional integration in the US dollar/euro exchange rate
Directory of Open Access Journals (Sweden)
Kiran Burcu
2012-01-01
Full Text Available This paper examines the nonlinear behavior and the fractional integration property of the US dollar/euro exchange rate over the period from January 1999 to August 2010 by extending the procedure of Peter M. Robinson (1994 to the case of nonlinearity. First, using the approach developed by Mehmet Caner and Bruce E. Hansen (2001, we investigate the possible presence of nonlinearity in the series through the estimation of a two-regime threshold autoregressive model. After finding nonlinearity, we also allow for disturbances to be fractionally integrated based on the different versions of Robinson (1994 tests. The findings show that the US dollar/euro exchange rate follows a stationary process with a weak evidence for long memory.
Krasilenko, Vladimir G.; Nikolsky, Alexander I.; Lazarev, Alexander A.; Lazareva, Maria V.
2008-03-01
In the paper the actuality of neurophysiologically motivated neuron arrays with flexibly programmable functions and operations with possibility to select required accuracy and type of nonlinear transformation and learning are shown. We consider neurons design and simulation results of multichannel spatio-time algebraic accumulation - integration of optical signals. Advantages for nonlinear transformation and summation - integration are shown. The offered circuits are simple and can have intellectual properties such as learning and adaptation. The integrator-neuron is based on CMOS current mirrors and comparators. The performance: consumable power - 100...500 μW, signal period- 0.1...1ms, input optical signals power - 0.2...20 μW time delays - less 1μs, the number of optical signals - 2...10, integration time - 10...100 of signal periods, accuracy or integration error - about 1%. Various modifications of the neuron-integrators with improved performance and for different applications are considered in the paper.
Directory of Open Access Journals (Sweden)
V. S. Serov
2010-01-01
Full Text Available A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.
Institute of Scientific and Technical Information of China (English)
郭金运; 陶华学
2003-01-01
In order to process different kinds of observing data with different precisions, a new solution model of nonlinear dynamic integral least squares adjustment was put forward, which is not dependent on their derivatives. The partial derivative of each component in the target function is not computed while iteratively solving the problem. Especially when the nonlinear target function is more complex and very difficult to solve the problem, the method can greatly reduce the computing load.
Classical Completely Integrable System Generated through Nonlinearization of an Eigenvalue Problem
Institute of Scientific and Technical Information of China (English)
LUOMant; LIXiu-li; XIANGMing-sen
2004-01-01
Under the Bargmann constrained condition, the spatial part of a new Lax pairof the higher order MkdV equation is nonlinearized to be a completely integrable system(R2N,dp∧dq, H0=1/2F0)(F0=〈Aq,p〉+〈Ap, p〉+〈p,q〉2). While the nonlinearization of the time part leads to its N-involutive system (Fm).
Directory of Open Access Journals (Sweden)
Jessada Tariboon
2014-01-01
Full Text Available We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented.
2014-01-09
nanoparticles (NPs) were added to luminescent porous silicon by drop casting. These NPs interact with this system by modifying its optical properties ...response by Au NPs in sapphire: Nonlinear optical response of Au metallic NPs, synthesized and embedded in sapphire by using ion implantation, as a...Linear and nonlinear plasmonics from isotropic and anisotropic integrated nanocomposites for quantum information applications. Jorge-Alejandro Reyes
Gorbach, Andrey V
2016-01-01
We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\\hbar\\omega=(2/3)E_F$.
Altet, J; Mateo, D; Perpiñà, X; Grauby, S; Dilhaire, S; Jordà, X
2011-09-01
This work presents an alternative characterization strategy to quantify the nonlinear behavior of temperature sensing systems. The proposed approach relies on measuring the temperature under thermal sinusoidal steady state and observing the intermodulation products that are generated within the sensing system itself due to its nonlinear temperature-output voltage characteristics. From such intermodulation products, second-order interception points can be calculated as a figure of merit of the measuring system nonlinear behavior. In this scenario, the present work first shows a theoretical analysis. Second, it reports the experimental results obtained with three thermal sensing techniques used in integrated circuits.
Extinction in neutrally stable stochastic Lotka-Volterra models.
Dobrinevski, Alexander; Frey, Erwin
2012-05-01
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.
Multivariate Moran process with Lotka-Volterra phenomenology.
Noble, Andrew E; Hastings, Alan; Fagan, William F
2011-11-25
For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This correspondence, on the one hand, allows us to infer the phenomenology of our Moran process based on much simpler Lokta-Volterra phenomenology and, on the other, allows us to study Lotka-Volterra dynamics within the finite populations of a Moran process. Applications to community ecology, population genetics, and evolutionary game theory are discussed.
Bahadur Zada, Mian; Sarwar, Muhammad; Radenović, Stojan
2017-01-01
In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].
Surface integrals approach to solution of some free boundary problems
Directory of Open Access Journals (Sweden)
Igor Malyshev
1988-01-01
Full Text Available Inverse problems in which it is required to determine the coefficients of an equation belong to the important class of ill-posed problems. Among these, of increasing significance, are problems with free boundaries. They can be found in a wide range of disciplines including medicine, materials engineering, control theory, etc. We apply the integral equations techniques, typical for parabolic inverse problems, to the solution of a generalized Stefan problem. The regularization of the corresponding system of nonlinear integral Volterra equations, as well as local existence, uniqueness, continuation of its solution, and several numerical experiments are discussed.
Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonlinear Sliding Surface
Directory of Open Access Journals (Sweden)
Yong-Kun Lu
2015-02-01
Full Text Available An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The stability of the controller is analyzed by Lyapunov stability theory. The effectiveness of the proposed speed regulator is demonstrated by the simulation results in comparison with the conventional integral sliding-mode controller based on boundary layer.
Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions.
Fokas, A S
2006-05-19
The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.
Classical and Quantum Nonlinear Integrable Systems: Theory and Application
Energy Technology Data Exchange (ETDEWEB)
Brzezinski, Tomasz [Department of Mathematics, University of Wales Swansea (United Kingdom)
2003-12-12
This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical
Local-instantaneous filtering in the integral transform solution of nonlinear diffusion problems
Macêdo, E. N.; Cotta, R. M.; Orlande, H. R. B.
A novel filtering strategy is proposed to be utilized in conjunction with the Generalized Integral Transform Technique (GITT), in the solution of nonlinear diffusion problems. The aim is to optimize convergence enhancement, yielding computationally efficient eigenfunction expansions. The proposed filters include space and time dependence, extracted from linearized versions of the original partial differential system. The scheme automatically updates the filter along the time integration march, as the required truncation orders for the user requested accuracy begin to exceed a prescribed maximum system size. A fully nonlinear heat conduction example is selected to illustrate the computational performance of the filtering strategy, against the classical single-filter solution behavior.
On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications
Directory of Open Access Journals (Sweden)
Kelong Cheng
2014-01-01
Full Text Available Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.
Global Format for Conservative Time Integration in Nonlinear Dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects: representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping with the purpose of extracting energy from undesirable high...... over the time step. This explicit formula is exact for structures with internal energy in the form of a polynomial in the displacement components of degree four. A fully general form follows by introducing an additional term based on a secant representation of the internal energy. The option......-frequency parts of the response. The energy conservation property is developed in two steps. First a fourth-order representation of the internal energy increment is obtained in terms of the mean value of the associated internal forces and an additional term containing the increment of the tangent stiffness matrix...
Nonlinear Optics in Optoelectronic Integration with Some Novel Waveguide Devices.
Vakhshoori, Daryoosh
By integration we mean realizing an integrable solution to existing discrete devices which perform some useful operation. Systems are built from these functional parts. System integration requires compatible integration of these parts. At present the most important example that also relates to our work is communication systems. For this system to work reliably, the optical pulses should be stable in time and shape (small time and amplitude jitter.) The devices that measure these properties are optical correlators. These devices are bulky, occupying a cubic foot of volume with no satisfactory integrable counterpart. Here we present an integrable waveguide correlator which experimentally measured pulses from 150fsec to 12psec with an average guide power of sub mW to 2mW in the spectral range of 1.7mum to 1.06mu m. All these measurements were performed on the same waveguide structure without mechanical movements where the spectral range was limited to the band gap of the waveguide material, GaAs in our case. The other communication scheme uses wavelength division multiplexing. Optical spectrometers are ~1 meter long devices capable of 0.1A spectral resolution. Again, like correlators, there is no satisfactory integrable counterpart. In this thesis, we present an integrable parametric waveguide spectrometer capable of measuring individual modes of semiconductor laser diodes and their movement as a function of laser current. For our experiments, the resolving power of the waveguide device was about 3A and is easily extendible to the sub A range. It should be pointed out that these spectrometer devices can also be used in stabilizing laser diode frequencies which are required for the realization of reliable wavelength division multiplexed systems. Last, but not least, a possible coherent visible surface emitting waveguide device capable of mW range powers is also presented. The motivation for this study is the ever growing market for shorter wavelength semiconductor
One-step block method for solving Volterra integro-differential equations
Mohamed, Nurul Atikah binti; Majid, Zanariah Abdul
2015-10-01
One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block method will solve the ordinary differential equations (ODEs) part and Newton-Cotes quadrature rule is applied to calculate the integral part of VIDEs. Numerical problems are presented to illustrate the performance of the proposed method.
The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice
Energy Technology Data Exchange (ETDEWEB)
Inoue, Rei [Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902 (Japan)
2004-01-30
We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes M{sub F} of polynomial matrices. Let X be the algebraic curve given by the common characteristic equation for M{sub F}. We construct the isomorphism from the set of representatives to an affine part of the Jacobi variety of X. This variety corresponds to the invariant manifold of the system, where the Hamiltonian flow is linearized. As an application, we discuss the algebraic complete integrability of the extended Lotka-Volterra lattice with a periodic boundary condition.
Volterra equation for pricing and hedging in a regime switching market
Directory of Open Access Journals (Sweden)
Anindya Goswami
2014-12-01
Full Text Available It is known that the risk minimizing price of European options in Markov-modulated market satisfies a system of coupled PDE, known as generalized B–S–M PDE. In this paper, another system of equations, which can be categorized as a Volterra integral equations of second kind, are considered. It is shown that this system of integral equations has smooth solution and the solution solves the generalized B–S–M PDE. Apart from showing existence and uniqueness of the PDE, this IE representation helps to develop a new computational method. It enables to compute the European option price and corresponding optimal hedging strategy by using quadrature method.
Persistence in periodic and almost periodic Lotka-Volterra systems.
Gopalsamy, K
1984-01-01
It is shown that a strongly self-regulating (or resource limited) Lotka-Volterra population system can "persist" in a periodic or almost periodic environment if and only if the system tracks the environmental variations.
On competitive Lotka–Volterra model in random environments
National Research Council Canada - National Science Library
Zhu, C; Yin, G
2009-01-01
Focusing on competitive Lotka-Volterra model in random environments, this paper uses regime-switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem...
Dynamics of a discrete Lotka-Volterra model
National Research Council Canada - National Science Library
Din, Qamar
2013-01-01
In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, and global behavior of equilibrium points of a discrete Lotka-Volterra model given by where parameters...
POSITIVE PERIODIC SOLUTIONS OFIMPULSIVE LATKA-VOLTERRA EQUATIONS
Institute of Scientific and Technical Information of China (English)
LiJianli; ShenJianhua
2005-01-01
By using the continuation of coincidence degree theory, we study the periodic Lotka-Volterra equations with impulses, and some sufficient onditions for the existence of positive periodic solutions are obtained.
PERMANENCE AND PERSISTENCE OF TIME VARYING LOTKA-VOLTERRA SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, the permanence and persistence for three classes time varying Lotka-Volterra ecological system are investigated by using Lyapunov stability analysis and constructing the compact set of attraction. Some examples are given to illustrate the theorems.
PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito' s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted.Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.
Nonlinear control for global stabilization of multiple-integrator system by bounded controls
Institute of Scientific and Technical Information of China (English)
Bin ZHOU; Guangren DUAN; Liu ZHANG
2008-01-01
The global stabilization problem of the multiple-integrator system by bounded controls is considered.A nonlinear feedback law consisting of nested saturation functions is proposed.This type of nonlinear feedback law that is a modification and generalization of the result given in[1] needs only[(n+1)/2](n is the dimensions of the system)saturation elements,which is fewer than that which the other nonlinear laws need.Funhermore.the poles of the closedloop system Can be placed on any location on the left real axis when none of the saturafion elements in the control laws is saturated.This type of nonlinear control law exhibits a simpler structure and call significantly improve the transient performances of the closed-loop system,and is very superior to the other existing methods.Simulation on a fourth-order system is used to validate the proposed method.
Nonlinear Optics in Doped Silica Glass Integrated Waveguide Structures
Duchesne, David; Razzari, Luca; Morandotti, Roberto; Little, Brent; Chu, Sai T; Moss, David J
2015-01-01
Integrated photonic technologies are rapidly becoming an important and fundamental milestone for wideband optical telecommunications. Future optical networks have several critical requirements, including low energy consumption, high efficiency, greater bandwidth and flexibility, which must be addressed in a compact form factor.
Food Web Assembly Rules for Generalized Lotka-Volterra Equations
DEFF Research Database (Denmark)
Härter, Jan Olaf Mirko; Mitarai, Namiko; Sneppen, Kim
2016-01-01
In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this......In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show...
[Analysis of seasonal fluctuations in the Lotka-Volterra model].
Lobanov, A I; Sarancha, D A; Starozhilova, T K
2002-01-01
A modification of the Lotka-Volterra model was proposed. The modification takes into account the factor of seasonal fluctuations in a "predator-prey" model. In this modification, interactions between species in summer are described by the Lotka-Volterra equations; in winter, individuals of both species extinct. This generalization makes the classic model unrough, which substantially extends the field of its application. The results of numerical simulation illustrate the statement formulated above.
Optoacoustic inversion via Volterra kernel reconstruction
Melchert, O; Roth, B
2016-01-01
In this letter we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we put under scrutiny the optoacoustic kernel reconstruction problem in the paraxial approximation of the underlying wave-equation. We apply a Fourier-series expansion of the optoacoustic Volterra kernel and obtain the respective expansion coefficients for a given "apparative" setup by performing a gauge procedure using synthetic input data. The resulting effective kernel is subsequently used to solve the optoacoustic source reconstruction problem for general signals. We verify the validity of the proposed inversion protocol for synthetic signals and explore the feasibility of our approach to also account for the diffraction transformation of signals beyond the paraxial approximation.
Ecological communities with Lotka-Volterra dynamics
Bunin, Guy
2017-04-01
Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.
Extinction in the Lotka-Volterra model.
Parker, Matthew; Kamenev, Alex
2009-08-01
Birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey interaction. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.
Conservative fourth-order time integration of non-linear dynamic systems
DEFF Research Database (Denmark)
Krenk, Steen
2015-01-01
An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating the re...... integration of oscillatory systems with only a few integration points per period. Three numerical examples demonstrate the high accuracy of the algorithm. (C) 2015 Elsevier B.V. All rights reserved.......An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...
Nonlinear dynamical systems of mathematical physics spectral and symplectic integrability analysis
Blackmore, Denis; Samoylenko, Valeriy Hr
2011-01-01
This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability,
Directory of Open Access Journals (Sweden)
Shoukry Ibrahim Atia El-Ganaini
2013-01-01
Full Text Available The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE, (2 + 1-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.
A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics
Wang, Xuechuan; Atluri, Satya N.
2017-05-01
A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac-Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method. These time integrators are labeled as Chebyshev local iterative collocation methods. Through examples of the forced Duffing oscillator, the Lorenz system, and the multiple coupled Duffing equations (which arise as semi-discrete equations for beams, plates and shells undergoing large deformations), it is shown that the new algorithms are far superior to the 4th order Runge-Kutta and ODE45 of MATLAB, in predicting the chaotic responses of strongly nonlinear dynamical systems.
A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics
Wang, Xuechuan; Atluri, Satya N.
2017-01-01
A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac-Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method. These time integrators are labeled as Chebyshev local iterative collocation methods. Through examples of the forced Duffing oscillator, the Lorenz system, and the multiple coupled Duffing equations (which arise as semi-discrete equations for beams, plates and shells undergoing large deformations), it is shown that the new algorithms are far superior to the 4th order Runge-Kutta and ODE45 of MATLAB, in predicting the chaotic responses of strongly nonlinear dynamical systems.
Saturations-based nonlinear controllers with integral term: validation in real-time
Alatorre, A. G.; Castillo, P.; Mondié, S.
2016-05-01
Popular saturations-based nonlinear controller usually include proportional and derivative components of the state or output. The fact that in many applications, these components do not suffice to insure the convergence to the desired output values, motivate the addition of an integral term. In this paper, three configurations of nonlinear controllers based on saturation functions are improved with an integral component. The stability of the three algorithms is analysed using the Lyapunov theory. Simulation results validate the proposed control laws when they are applied to nonlinear systems with constant and unknown perturbations. Real-time experiments realised with a quad-rotor aerial vehicle and a hovercraft vehicle show that the proposed scheme can follow autonomously some trajectories, and that it could be robust with respect to delays.
Fokas, A. S.; De Lillo, S.
2014-03-01
So-called inverse scattering provides a powerful method for analyzing the initial value problem for a large class of nonlinear evolution partial differential equations which are called integrable. In the late 1990s, the first author, motivated by inverse scattering, introduced a new method for analyzing boundary value problems. This method provides a unified treatment for linear, linearizable and integrable nonlinear partial differential equations. Here, this method, which is often referred to as the unified transform, is illustrated for the following concrete cases: the heat equation on the half-line; the nonlinear Schrödinger equation on the half-line; Burger's equation on the half-line; and Burger's equation on a moving boundary.
Lattice defects as Lotka-Volterra societies
Energy Technology Data Exchange (ETDEWEB)
Yost, F.G.
1995-07-01
Since the early part of this century the Lotka-Volterra or predator-prey equations have been known to simulate the stability, instability, and persistent oscillations observed in many biological and ecological societies. These equations have been modified in many ways and have been used to model phenomena as varied as childhood epidemics, enzyme reactions, and conventional warfare. In the work to be described, similarities are drawn between various lattice defects and Lotka-Volterra (LV) societies. Indeed, grain boundaries are known to ``consume`` dislocations, inclusions ``infect`` grain boundaries, and dislocations ``annihilate`` dislocations. Several specific cases of lattice defect interaction kinetics models are drawn from the materials science literature to make these comparisons. Each model will be interpreted as if it were a description of a biological system. Various approaches to the modification of this class of interaction kinetics will be presented and discussed. The earliest example is the Damask-Dienes treatment of vacancy-divacancy annealing kinetics. This historical model will be modified to include the effects of an intermediate species and the results will be compared with the original model. The second example to be examined is the Clark-Alden model for deformation-enhanced grain growth. Dislocation kinetics will be added to this model and results will be discussed considering the original model. The third example to be presented is the Ananthakrishna-Sahoo model of the Portevin-Le Chatelier effect that was offered in 1985 as an extension of the classical Cottrell atmosphere explanation. Their treatment will be modified by inclusion of random interference from a pesky but peripheral species and by allowing a rate constant to be a function of time.
Dynamic Sliding Mode Control Design Based on an Integral Manifold for Nonlinear Uncertain Systems
Qudrat Khan; Aamer Iqbal Bhatti; Antonella Ferrara
2014-01-01
An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In c...
Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.
2017-08-01
We have proposed an algorithm for the sequential construction of nonisotropic matrix elements of the collision integral, which are required to solve the nonlinear Boltzmann equation using the moments method. The starting elements of the matrix are isotropic and assumed to be known. The algorithm can be used for an arbitrary law of interactions for any ratio of the masses of colliding particles.
Directory of Open Access Journals (Sweden)
Jiqiang Jiang
2012-01-01
Full Text Available We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results.
Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem
Directory of Open Access Journals (Sweden)
Benaicha Slimane
2016-07-01
Full Text Available In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.
A STUDY ON SOME PROBLEMS ON EXISTENCE OF SOLUTIONS FOR NONLINEAR FUNCTIONAL-INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
DEEPMALA; H.K. PATHAK
2013-01-01
In this paper, we prove the existence of solutions of some nonlinear functional-integral equation by using a fixed point theorem which satisfy the Darbo condition. The results extend the corresponding results of many authors. In the sequel, we give an example of our main result to highlight the realized improvements.
Classical integrability of the O(N) nonlinear $\\sigma$ model on a half-line
Corrigan, E
1996-01-01
The classical integrability the O(N) nonlinear sigma model on a half-line is examined, and the existence of an infinity of conserved charges in involution is established for the free boundary condition. For the case N=3 other possible boundary conditions are considered briefly.
Response of Non-Linear Systems to Renewal Impulses by Path Integration
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Iwankiewicz, R.
The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal...... additional discrete-valued state variables for which the stochastic equations are also formulated....
New solutions for two integrable cases of a generalized fifth-order nonlinear equation
Wazwaz, Abdul-Majid
2015-05-01
Multiple-complexiton solutions for a new generalized fifth-order nonlinear integrable equation are constructed with the help of the Hirota's method and the simplified Hirota's method. By extending the real parameters into complex parameters, nonsingular complexiton solutions are obtained for two specific coefficients of the new generalized equation.
Song, Dong; Robinson, Brian S; Hampson, Robert E; Marmarelis, Vasilis Z; Deadwyler, Sam A; Berger, Theodore W
2015-01-01
In order to build hippocampal prostheses for restoring memory functions, we build multi-input, multi-output (MIMO) nonlinear dynamical models of the human hippocampus. Spike trains are recorded from the hippocampal CA3 and CA1 regions of epileptic patients performing a memory-dependent delayed match-to-sample task. Using CA3 and CA1 spike trains as inputs and outputs respectively, second-order sparse generalized Laguerre-Volterra models are estimated with group lasso and local coordinate descent methods to capture the nonlinear dynamics underlying the spike train transformations. These models can accurately predict the CA1 spike trains based on the ongoing CA3 spike trains and thus will serve as the computational basis of the hippocampal memory prosthesis.
Papadopoulos, Agathoklis; Kostoglou, Kyriaki; Mitsis, Georgios D; Theocharides, Theocharis
2015-01-01
The use of a GPGPU programming paradigm (running CUDA-enabled algorithms on GPU cards) in biomedical engineering and biology-related applications have shown promising results. GPU acceleration can be used to speedup computation-intensive models, such as the mathematical modeling of biological systems, which often requires the use of nonlinear modeling approaches with a large number of free parameters. In this context, we developed a CUDA-enabled version of a model which implements a nonlinear identification approach that combines basis expansions and polynomial-type networks, termed Laguerre-Volterra networks and can be used in diverse biological applications. The proposed software implementation uses the GPGPU programming paradigm to take advantage of the inherent parallel characteristics of the aforementioned modeling approach to execute the calculations on the GPU card of the host computer system. The initial results of the GPU-based model presented in this work, show performance improvements over the original MATLAB model.
Global attractor of coupled difference equations and applications to Lotka-Volterra systems
Directory of Open Access Journals (Sweden)
Pao CV
2005-01-01
Full Text Available This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution.
Global attractor of coupled difference equations and applications to Lotka-Volterra systems
Directory of Open Access Journals (Sweden)
C. V. Pao
2005-03-01
Full Text Available This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution.
Gutierrez, Alberto, Jr.
1995-01-01
This dissertation evaluates receiver-based methods for mitigating the effects due to nonlinear bandlimited signal distortion present in high data rate satellite channels. The effects of the nonlinear bandlimited distortion is illustrated for digitally modulated signals. A lucid development of the low-pass Volterra discrete time model for a nonlinear communication channel is presented. In addition, finite-state machine models are explicitly developed for a nonlinear bandlimited satellite channel. A nonlinear fixed equalizer based on Volterra series has previously been studied for compensation of noiseless signal distortion due to a nonlinear satellite channel. This dissertation studies adaptive Volterra equalizers on a downlink-limited nonlinear bandlimited satellite channel. We employ as figure of merits performance in the mean-square error and probability of error senses. In addition, a receiver consisting of a fractionally-spaced equalizer (FSE) followed by a Volterra equalizer (FSE-Volterra) is found to give improvement beyond that gained by the Volterra equalizer. Significant probability of error performance improvement is found for multilevel modulation schemes. Also, it is found that probability of error improvement is more significant for modulation schemes, constant amplitude and multilevel, which require higher signal to noise ratios (i.e., higher modulation orders) for reliable operation. The maximum likelihood sequence detection (MLSD) receiver for a nonlinear satellite channel, a bank of matched filters followed by a Viterbi detector, serves as a probability of error lower bound for the Volterra and FSE-Volterra equalizers. However, this receiver has not been evaluated for a specific satellite channel. In this work, an MLSD receiver is evaluated for a specific downlink-limited satellite channel. Because of the bank of matched filters, the MLSD receiver may be high in complexity. Consequently, the probability of error performance of a more practical
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-07
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability
Conservative fourth-order time integration of non-linear dynamic systems
DEFF Research Database (Denmark)
Krenk, Steen
2015-01-01
An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating the re...... integration of oscillatory systems with only a few integration points per period. Three numerical examples demonstrate the high accuracy of the algorithm. (C) 2015 Elsevier B.V. All rights reserved.......An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...
Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.
Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong
2014-12-01
In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.
Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.
Integral sliding mode control for a class of nonlinear neutral systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Lou Xu-Yang; Cui Bao-Tong
2008-01-01
This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feasibility of the proposed technique.
On approximation of nonlinear boundary integral equations for the combined method
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1989-09-22
The nonlinear boundary integral equations that arise in research of nonlinear magnetostatic problems are investigated in combined formulation on an unbounded domain. Approximations of the derived operator equations are studied based on the Galerkin method. The investigated boundary operators are strongly monotone, Lipschitz-continuous, potential and have a symmetrical Gateaux derivative. The error estimates of the Galerkin's approximation in Sobolev spaces of fractional powers are obtained using the above-mentioned properties of the operators, too. The problem has been studied on surfaces in two and three-dimensional spaces. We answer also some questions on convergence connected with the discretized systems of equations. 21 refs.
Ulku, Huseyin Arda
2014-07-06
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half
Energy Technology Data Exchange (ETDEWEB)
Moriceau, Y. [Commissariat a l' Energie Atomique, Centre d' Etudes de Limeil, 94 - Villeneuve-Saint-Georges (France)
1968-03-01
It is well known, if not well explained, that photo cross-sections curves depend on numerical resolution; as well as many other physical solutions from integral equations of the first kind, they are oscillating. In the first part of this report, a typical example points out how oscillations are growing. In the second part, a new method is explained yielding a smooth resolution. From experimental data on equidistant intervals, we build functions expanded in Tchebycheff polynomials; the solution is of this kind. Then, the third part points out that semi-analytical resolutions of this problem are illusive. (author) [French] C'est un fait reconnu mais mal explique, que les courbes de sections efficaces photonucleaires dependent de la resolution numerique adoptee. Beaucoup d'autres solutions physiques extraites d'une equation integrale de 1ere espece sont dans ce cas; elles sont arbitraires et oscillatoires. Dans la 1ere partie de ce rapport, on montre, dans un cas particulier typique, comment se forment les oscillations. Dans la 2eme partie, on presente une methode originale qui permet d'obtenir une resolution exempte d'oscillations. A partir de donnees experimentales a intervalles equidistants, on construit des fonctions developpees en polynomes de Tchebycheff; la solution est de ce type. Enfin, on montre dans la 3eme partie que les resolutions semi-analytiques de ce probleme sont illusoires. (auteur)
Directory of Open Access Journals (Sweden)
Ali Konuralp
2014-01-01
Full Text Available Application process of variational iteration method is presented in order to solve the Volterra functional integrodifferential equations which have multi terms and vanishing delays where the delay function θ(t vanishes inside the integral limits such that θ(t=qt for 0
Hydex Glass and Amorphous Silicon for Integrated Nonlinear Optical Signal Processing
Morandotti, Roberto
2015-01-01
Photonic integrated circuits that exploit nonlinear optics in order to generate and process signals all-optically have achieved performance far superior to that possible electronically - particularly with respect to speed. Although silicon-on-insulator has been the leading platform for nonlinear optics for some time, its high two-photon absorption at telecommunications wavelengths poses a fundamental limitation. We review the recent achievements based in new CMOS-compatible platforms that are better suited than SOI for nonlinear optics, focusing on amorphous silicon and Hydex glass. We highlight their potential as well as the challenges to achieving practical solutions for many key applications. These material systems have opened up many new capabilities such as on-chip optical frequency comb generation and ultrafast optical pulse generation and measurement.
Nonlinear adaptive control using the Fourier integral and its application to CSTR systems.
Zhang, Huaguang; Cai, Lilong
2002-01-01
This paper presents a new nonlinear adaptive tracking controller for a class of general time-variant nonlinear systems. The control system consists of an inner loop and an outer loop. The inner loop is a fuzzy sliding mode control that is used as the feedback controller to overcome random instant disturbances. The stability of the inner loop is designed by the sliding mode control method. The other loop is a Fourier integral-based control that is used as the feedforward controller to overcome the deterministic type of uncertain disturbance. The asymptotic convergence condition of the nonlinear adaptive control system is guaranteed by the Lyapunov direct method. The effectiveness of the proposed controller is illustrated by its application to composition control in a continuously stirred tank reactor system.
Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models
Hisakado, M
1998-01-01
We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.
Institute of Scientific and Technical Information of China (English)
LI Xuezhi; GENI Gupur; ZHU Guangtian
2001-01-01
In this paper, a set of sufficient conditions is obtained for the ultimate boundedness of nonautonomous n-species diffusive Lotka-Volterra sub-models in two heterogeneous patches. The sub-models are the Lotka-Volterra tree systems, including the Lotka-Volterra chain systems and the Lotka-Volterra models between one and multispecies. The criteria in this paper are in explicit forms of the parameters and thus are easily verifiable.
Semiotic Interpretation of Lotka–Volterra Model and its Usage in Knowledge Management
Directory of Open Access Journals (Sweden)
Evdokimov Kirill E.
2016-01-01
Full Text Available Convergence of NBICS-technologies makes relevant the exact definition of objective goals’ spectrum, which pursued this self-organizing system of technologies. Authors consider the objective goals of this system of technologies as “semiotic attractors” and the tasks related to knowledge management at the NBICS-technologies niche as management of competition between the goals, which cause processes of creation, transmission, reception, usage and duplication of the new knowledge. Competitive interaction of these goals (and their symbolizations were researched on the grounds of Lotka–Volterra model. The original interpretation of Lotka–Volterra model is posed on the basis of stated interconnection between the stages of complex systems’ non-linear dynamics, this self-organization’s information mechanisms and the semiotic results of information processes’ stages. This synthesis of synergetic, cybernetic and semiotic paradigms is implemented on the grounds of A. N. Whitehead process philosophy. Semiotic interpretation of the model allowed determining the order of goals’ conversion and defining the stages of dynamics at which this transformation by means of knowledge management is constructive.
A PREDICT-CORRECT NUMERICAL INTEGRATION SCHEME FOR SOLVING NONLINEAR DYNAMIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Fan Jianping; Huang Tao; Tang Chak-yin; Wang Cheng
2006-01-01
A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equaton (v) = F(v, t) was transformed into the form as (v) = Hv+ f(v, t). The nonlinear part f(v, t) was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.
Monitoring in a Lotka-Volterra model.
López, I; Gámez, M; Garay, J; Varga, Z
2007-01-01
The problem of monitoring arises when in an ecosystem, in particular in a system of several populations, observing some components, we want to recover the state of the whole system as a function of time. Due to the difficulty to construct exactly this state process, we look for an auxiliary system called an observer. This system reproduces this process with a certain approximation. This means that the solution of the observer tends to that of the original system. An important concept for this work is observability. This means that from the observation it is possible to recover uniquely the state process, however, without determining a constructive method to obtain it. If observability holds for the original system, it guarantees the existence of an auxiliary matrix that makes it possible to construct an observer of the system. The considered system of populations is described by the classical Lotka-Volterra model with one predator and two preys and the construction of its observer is illustrated with a numerical example. Finally, it is shown how the observer can be used for the estimation of the level of an abiotic effect on the population system.
Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics
2016-01-01
This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application...
Global format for energy-momentum based time integration in nonlinear dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... in fourth‐order form consisting of the end‐point mean value plus a term containing the stiffness matrix increment. This form gives energy conservation for systems with internal energy as a quartic function of the displacement components. This representation is then extended to general energy conservation...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...
Yang, Yunqing; Malomed, Boris A
2015-01-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel (LPD) equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Energy Technology Data Exchange (ETDEWEB)
Zenchuk, A I, E-mail: zenchuk@itp.ac.r [Institute of Problems of Chemical Physics, RAS Acad. Semenov av., 1 Chernogolovka, Moscow region 142432 (Russian Federation)
2010-06-18
We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical C- and S-integrable partial differential equations (PDEs). Generalizations of (1+1)-dimensional C-integrable and (2+1)-dimensional S-integrable N-wave equations are derived among examples. Examples of multidimensional second-order PDEs are represented as well.
Representation of neural networks as Lotka-Volterra systems
Moreau, Yves; Louiès, Stéphane; Vandewalle, Joos; Brenig, Léon
1999-03-01
We study changes of coordinates that allow the representation of the ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models—also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form, where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoïd. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network.
Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras
Grahovski, Georgi G.; Mikhailov, Alexander V.
2013-12-01
Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of these Darboux transformations leads to integrable Grassmann generalisations of the difference Toda and NLS equations. The resulting systems will have discrete Lax representations provided by the set of two consistent elementary Darboux transformations. For the two discrete systems obtained, initial value and initial-boundary problems are formulated.
Integrable Discretisations for a Class of Nonlinear Schrodinger Equations on Grassmann Algebras
Grahovski, Georgi G
2013-01-01
Integrable discretisations for a class of coupled nonlinear Schrodinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of these Darboux transformations leads to integrable Grassmamm generalisations of the difference Toda and NLS equations. The resulting discrete systems will have Lax pairs provided by the set of two consistent Darboux transformations.
Directory of Open Access Journals (Sweden)
Lijun Zhang
2014-01-01
Full Text Available An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions. The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.
Time-Domain Volume Integral Equation for TM-Case Scattering from Nonlinear Penetrable Objects
Institute of Scientific and Technical Information of China (English)
WANG Jianguo; Eric Michielssen
2001-01-01
This paper presents the time-domainvolume integral equation (TDVIE) method to analyzescattering from nonlinear penetrable objects, whichare illuminated by the transverse magnetic (TM) in-cident pulse. The time-domain volume integral equa-tion is formulated in terms of two-dimensional (2D)Green's function, and solved by using the march-on-in time (MOT) technique. Some numerical results aregiven to validate this method, and comparisons aremade with the results obtained by using the finite-difference time-domain (FDTD) method.
Institute of Scientific and Technical Information of China (English)
ZHANG Suying; DENG Zichen
2005-01-01
Based on Magnus or Fer expansion for solving linear differential equation and operator semi-group theory, Lie group integration methods for general nonlinear dynamic equation are studied. Approximate schemes of Magnus type of 4th, 6th and 8th order are constructed which involve only 1, 4 and 10 different commutators, and the time-symmetry properties of the schemes are proved. In the meantime, the integration methods based on Fer expansion are presented. Then by connecting the Fer expansion methods with Magnus expansion methods some techniques are given to simplify the construction of Fer expansion methods. Furthermore time-symmetric integrators of Fer type are constructed. These methods belong to the category of geometric integration methods and can preserve many qualitative properties of the original dynamic system.
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2012-01-01
Full Text Available In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.
Competitive Lotka-Volterra Population Dynamics with Jumps
Bao, Jianhai; Yin, Geroge; Yuan, Chenggui
2011-01-01
This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) We discuss the uniform boundedness of $p$th moment with $p>0$ and reveal the sample Lyapunov exponents; (c) Using a variation-of-constants formula for a class of SDEs with jumps, we provide explicit solution for 1-dimensional competitive Lotka-Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our $n$-dimensional model.
Directory of Open Access Journals (Sweden)
Susmita Paul
2016-03-01
Full Text Available This paper reflects some research outcome denoting as to how Lotka–Volterra prey predator model has been solved by using the Runge–Kutta–Fehlberg method (RKF. A comparison between Runge–Kutta–Fehlberg method (RKF and the Laplace Adomian Decomposition method (LADM is carried out and exact solution is found out to verify the applicability, efficiency and accuracy of the method. The obtained approximate solution shows that the Runge–Kutta–Fehlberg method (RKF is a more powerful numerical technique for solving a system of nonlinear differential equations.
A novel identification method of Volterra series in rotor-bearing system for fault diagnosis
Xia, Xin; Zhou, Jianzhong; Xiao, Jian; Xiao, Han
2016-01-01
Volterra series is widely employed in the fault diagnosis of rotor-bearing system to prevent dangerous accidents and improve economic efficiency. The identification of the Volterra series involves the infinite-solution problems which is caused by the periodic characteristic of the excitation signal of rotor-bearing system. But this problem has not been considered in the current identification methods of the Volterra series. In this paper, a key kernels-PSO (KK-PSO) method is proposed for Volterra series identification. Instead of identifying the Volterra series directly, the key kernels of Volterra are found out to simply the Volterra model firstly. Then, the Volterra series with the simplest formation is identified by the PSO method. Next, simulation verification is utilized to verify the feasibility and effectiveness of the KK-PSO method by comparison to the least square (LS) method and traditional PSO method. Finally, experimental tests have been done to get the Volterra series of a rotor-bearing test rig in different states, and a fault diagnosis system is built with a neural network to classify different fault conditions by the kernels of the Volterra series. The analysis results indicate that the KK-PSO method performs good capability on the identification of Volterra series of rotor-bearing system, and the proposed method can further improve the accuracy of fault diagnosis.
Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2015-05-01
This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods.
Volterra series based predistortion for broadband RF power amplifiers with memory effects
Institute of Scientific and Technical Information of China (English)
Jin Zhe; Song Zhihuan; He Jiaming
2008-01-01
RF power amplifiers(PAs)are usually considered as memoryless devices in most existing predistortion techniques.However,in broadband communication systems,such as WCDMA,the PA memory effects are significant,and memoryless predistortion cannot linearize the PAs effectively.After analyzing the PA memory effects,a novel predistortion method based on the simplified Volterra series is proposed to linearize broadband RF PAs with memory effects.The indirect learning architecture is adopted to design the predistortion scheme and the recursive least squares algorithm with forgetting factor is applied to identify the parameters of the predistorter.Simulation results show that the proposed predistortion method can compensate the nonlinear distortion and memory effects of broadband RF PAs effectively.
Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.
Bendahmane, Mostafa; Ruiz-Baier, Ricardo; Tian, Canrong
2016-05-01
In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.
Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems
Institute of Scientific and Technical Information of China (English)
John E.D.EKORU; Jimoh O.PEDRO
2013-01-01
This paper presents the development of a proportional-integral-derivative (PID)-based control method for application to active vehicle suspension systems (AVSS).This method uses an inner PID hydraulic actuator force control loop,in combination with an outer PID suspension travel control loop,to control a nonlinear half-car AVSS.Robustness to model uncertainty in the form of variation in suspension damping is tested,comparing performance of the AVSS with a passive vehicle suspension system (PVSS),with similar model parameters.Spectral analysis of suspension system model output data,obtained by performing a road input disturbance frequency sweep,provides frequency response plots for both nonlinear vehicle suspension systems and time domain vehicle responses to a sinusoidal road input disturbance on a smooth road.The results show the greater robustness of the AVSS over the PVSS to parametric uncertainty in the frequency and time domains.
Photonic Damascene Process for Integrated High-Q Microresonator Based Nonlinear Photonics
Pfeiffer, Martin H P; Brasch, Victor; Zervas, Michael; Geiselmann, Michael; Jost, John D; Kippenberg, Tobias J
2015-01-01
High confinement, integrated silicon nitride (SiN) waveguides have recently emerged as attractive platform for on-chip nonlinear optical devices. The fabrication of high-Q SiN microresonators with anomalous group velocity dispersion (GVD) has enabled broadband nonlinear optical frequency comb generation. Such frequency combs have been successfully applied in coherent communication and ultrashort pulse generation. However, the reliable fabrication of high confinement waveguides from stoichiometric, high stress SiN remains challenging. Here we present a novel photonic Damascene fabrication process enabling the use of substrate topography for stress control and thin film crack prevention. With close to unity sample yield we fabricate microresonators with $1.35\\,\\mu\\mathrm{m}$ thick waveguides and optical Q factors of $3.7\\times10^{6}$ and demonstrate single temporal dissipative Kerr soliton (DKS) based coherent optical frequency comb generation. Our newly developed process is interesting also for other material ...
Directory of Open Access Journals (Sweden)
MANFREDI, P.
2014-11-01
Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.
On the symplectic integration of the discrete nonlinear Schr\\"odinger equation with disorder
Gerlach, Enrico; Skokos, Charalampos
2015-01-01
We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\\"{o}dinger (DDNLS) equation, and compare their efficiency. Our results suggest that the most suitable methods for the very long time integration of this one-dimensional Hamiltonian lattice model with many degrees of freedom (of the order of a few hundreds) are the ones based on three part splits of the system's Hamiltonian. Two part split techniques can be preferred for relatively small lattices having up to $N\\approx\\;$70 sites. An advantage of the latter methods is the better conservation of the system's second integral, i.e.~the wave packet's norm.
Implicit objective integration for sensitivity analysis in non-linear solid mechanics
Leu, Liang-Jeno; Mukherjee, Subrata
1994-11-01
Incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with both material and geometrical non-linearities. The derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class. Two widely used objective stress rates, the Jaumann rate and the Green-Naghdi rate, are considered here within the only minor changes of the integration scheme. Numerical results are presented for a simple shear problem with different material consititutive laws, including a hypoelastic model and a isotropic viscoplastic model, for these two objective rates. The num0rical results are compared with analytical solutions or direct integration solutions. The close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme.
Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System
Directory of Open Access Journals (Sweden)
Yue-Wen Cheng
2013-01-01
Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.
The Asymptotic Behavior for Numerical Solution of a Volterra Equation
Institute of Scientific and Technical Information of China (English)
Da Xu
2003-01-01
Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered.
Coexistence and exclusion of stochastic competitive Lotka-Volterra models
Nguyen, Dang H.; Yin, George
2017-02-01
This work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model. The conditions obtained are close to necessary. In addition, convergence in distribution of positive solutions of the model is also established. A number of numerical examples are given to illustrate our results.
Dynamic deviation Volterra predistorter designed for linearizing power amplifiers
2011-01-01
Polynomial models of predistorter combined by the "black box" principle have been considered. A Volterra model using one-dimensional dynamic deviation was proposed. An adaptive predistorter was synthesized for linearizing the Wiener–Hammerstein model of power amplifiers. Estimates of the linearization accuracy and a comparative analysis of predistorter models were also presented.
Evolution of Black-Box Models Based on Volterra Series
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Daniel D. Silveira
2015-01-01
Full Text Available This paper presents a historical review of the many behavioral models actually used to model radio frequency power amplifiers and a new classification of these behavioral models. It also discusses the evolution of these models, from a single polynomial to multirate Volterra models, presenting equations and estimation methods. New trends in RF power amplifier behavioral modeling are suggested.
A Lotka-Volterra competition model with seasonal succession.
Hsu, Sze-Bi; Zhao, Xiao-Qiang
2012-01-01
A complete classification for the global dynamics of a Lotka-Volterra two species competition model with seasonal succession is obtained via the stability analysis of equilibria and the theory of monotone dynamical systems. The effects of two death rates in the bad season and the proportion of the good season on the competition outcomes are also discussed. © Springer-Verlag 2011
Permanence and global attractivity for Lotka-Volterra difference systems.
Lu, Z; Wang, W
1999-09-01
The permanence and global attractivity for two-species difference systems of Lotka-Volterra type are considered. It is proved that a cooperative system cannot be permanent. For a permanent competitive system, the explicit expression of the permanent set E is obtained and sufficient conditions are given to guarantee the global attractivity of the positive equilibrium of the system.
Directory of Open Access Journals (Sweden)
Douglas Zhou
Full Text Available It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as V(S(Exp ≈ V(E(Exp + V(I(Exp + kV(E(Exp V(I(Exp, where V(S(Exp, V(E(Exp and V(I(Exp are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient k in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient k by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.
Intrinsic Nonlinearities and Layout Impacts of 100 V Integrated Power MOSFETs in Partial SOI Process
DEFF Research Database (Denmark)
Fan, Lin; Knott, Arnold; Jørgensen, Ivan Harald Holger
Parasitic capacitances of power semiconductors are a part of the key design parameters of state-of-the-art very high frequency (VHF) power supplies. In this poster, four 100 V integrated power MOSFETs with different layout structures are designed, implemented, and analyzed in a 0.18 ȝm partial...... Silicon-on-Insulator (SOI) process with a die area 2.31 mm2. A small-signal model of power MOSFETs is proposed to systematically analyze the nonlinear parasitic capacitances in different transistor states: off-state, sub-threshold region, and on-state in the linear region. 3D plots are used to summarize...
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Ying Wang
2015-03-01
Full Text Available In this article, we study the existence of multiple positive solutions for singular semipositone boundary-value problem (BVP with integral boundary conditions on infinite intervals. By using the properties of the Green's function and the Guo-Krasnosel'skii fixed point theorem, we obtain the existence of multiple positive solutions under conditions concerning the nonlinear functions. The method in this article can be used for a large number of problems. We illustrate the validity of our results with an example in the last section.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics
Lam, F
2013-01-01
A vorticity theory for incompressible fluid flows in the absence of solid boundaries is proposed. Some apriori bounds are established. They are used in an interpolation theory to show the well-posedness of the vorticity Cauchy problem. A non-linear integral equation for vorticity is derived and its solution is expressed in an expansion. Interpretations of flow evolutions starting from given initial data are given and elaborated. The kinetic theory for Maxwellian molecules with cut-off is revisited in order to link microscopic properties to flow characters on the continuum.
Input-Dependent Integral Nonlinearity Modeling for Pipelined Analog-Digital Converters
Samer Medawar; Peter Händel; Niclas Björsell; Magnus Jansson
2010-01-01
Integral nonlinearity (INL) for pipelined analog-digital converters (ADCs) operating at RF is measured and characterized. A parametric model for the INL of pipelined ADCs is proposed, and the corresponding least-squares problem is formulated and solved. The INL is modeled both with respect to the converter output code and the frequency stimuli, which is dynamic modeling. The INL model contains a static and a dynamic part. The former comprises two 1-D terms in ADC code that are a sequence of z...
A multiple-scale power series method for solving nonlinear ordinary differential equations
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Chein-Shan Liu
2016-02-01
Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.
On a method for constructing the Lax pairs for nonlinear integrable equations
Habibullin, I. T.; Khakimova, A. R.; Poptsova, M. N.
2016-01-01
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found immediately, coinciding with the linearization of the considered nonlinear equation. The second one is obtained as an invariant manifold to the linearized equation. A surprisingly simple relation between the second operator of the Lax pair and the recursion operator is discussed: the recursion operator can immediately be found from the Lax pair. Examples considered in the article are convincing evidence that the found Lax pairs differ from the classical ones. The examples also show that the suggested objects are true Lax pairs which allow the construction of infinite series of conservation laws and hierarchies of higher symmetries. In the case of the hyperbolic type partial differential equation our algorithm is slightly modified; in order to construct the Lax pairs from the invariant manifolds we use the cutting off conditions for the corresponding infinite Laplace sequence. The efficiency of the method is illustrated by application to some equations given in the Svinolupov-Sokolov classification list for which the Lax pairs and the recursion operators have not been found earlier.
Parametric characteristic of the random vibration response of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Xing-Jian Dong; Zhi-Ke Peng; Wen-Ming Zhang; Guang Meng; Fu-Lei Chu
2013-01-01
Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of non-linear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density (PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study
Botelho, Luiz Carlos Lobato
2010-01-01
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.
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Mahmood Pervaiz
2014-01-01
Full Text Available We present a control strategy for nonlinear nontriangular uncertain systems. The proposed control method is a synergy between the dynamic adaptive backstepping (DAB and integral sliding mode (ISM and is referred to as DAB-ISMC. Our main objective is to find a recursive procedure to transform a nontriangular system into an implementable form that enables designing a control law which almost eliminates the reaching-phase. The proposed method further facilitates minimization of chattering which is believed to be a shortcoming of the sliding mode control. In this methodology, the ISM, as an integrated subsystem of DAB, is introduced at the final stage of backstepping. This strategy works very well to obtain a system that is robust against model imperfections, matching and unmatching uncertainties. The DAB-ISMC method is applied on a continuous stirred tank reactor (CSTR and simulation results obtained on Matlab are found to be very promising.
Energy Technology Data Exchange (ETDEWEB)
Stancari, G. [Fermilab; Carlson, K. [Fermilab; McGee, M. W. [Fermilab; Nobrega, L. E. [Fermilab; Romanov, A. L. [Fermilab; Ruan, J. [Fermilab; Valishev, A. [Fermilab; Noll, D. [Frankfurt U.
2015-06-01
Recent developments in the study of integrable Hamiltonian systems have led to nonlinear accelerator lattice designs with two transverse invariants. These lattices may drastically improve the performance of high-power machines, providing wide tune spreads and Landau damping to protect the beam from instabilities, while preserving dynamic aperture. To test the feasibility of these concepts, the Integrable Optics Test Accelerator (IOTA) is being designed and built at Fermilab. One way to obtain a nonlinear integrable lattice is by using the fields generated by a magnetically confined electron beam (electron lens) overlapping with the circulating beam. The parameters of the required device are similar to the ones of existing electron lenses. We present theory, numerical simulations, and first design studies of electron lenses for nonlinear integrable optics.
Direct and inverse solver for the 3D optoacoustic Volterra equation
Stritzel, J; Wollweber, M; Roth, B
2016-01-01
The direct problem of optoacoustic signal generation in biological media consists of solving the inhomogeneous optoacoustic wave equation for an initial acoustic stress profile. In contrast, the mathematically challenging inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider the particular case of a Gaussian transverse irradiation source profile in the paraxial approximation of the wave equation, for which the direct problem along the beam axis can be cast into a linear Volterra integral equation of the second kind. This integral equation can be used in two ways: as a forward solver to predict optoacoustic signals in terms of the direct problem, and as an inverse solver for which we here devise highly efficient numerical schemes used for the reconstruction of initial pressure profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity...
Directory of Open Access Journals (Sweden)
Taochang Li
2014-01-01
Full Text Available Automatic steering control is the key factor and essential condition in the realization of the automatic navigation control of agricultural vehicles. In order to get satisfactory steering control performance, an adaptive sliding mode control method based on a nonlinear integral sliding surface is proposed in this paper for agricultural vehicle steering control. First, the vehicle steering system is modeled as a second-order mathematic model; the system uncertainties and unmodeled dynamics as well as the external disturbances are regarded as the equivalent disturbances satisfying a certain boundary. Second, a transient process of the desired system response is constructed in each navigation control period. Based on the transient process, a nonlinear integral sliding surface is designed. Then the corresponding sliding mode control law is proposed to guarantee the fast response characteristics with no overshoot in the closed-loop steering control system. Meanwhile, the switching gain of sliding mode control is adaptively adjusted to alleviate the control input chattering by using the fuzzy control method. Finally, the effectiveness and the superiority of the proposed method are verified by a series of simulation and actual steering control experiments.
Distinguishing linear vs. nonlinear integration in CA1 radial oblique dendrites: it’s about time
Directory of Open Access Journals (Sweden)
José Francisco eGómez González
2011-11-01
Full Text Available It was recently shown that multiple excitatory inputs to CA1 pyramidal neuron dendrites must be activated nearly simultaneously to generate local dendritic spikes and superlinear responses at the soma; even slight input desynchronization prevented local spike initiation (Gasparini, 2006;Losonczy, 2006. This led to the conjecture that CA1 pyramidal neurons may only express their nonlinear integrative capabilities during the highly synchronized sharp waves and ripples that occur during slow wave sleep and resting/consummatory behavior, whereas during active exploration and REM sleep (theta rhythm, inadequate synchronization of excitation would lead CA1 pyramidal cells to function as essentially linear devices. Using a detailed single neuron model, we replicated the experimentally observed synchronization effect for brief inputs mimicking single synaptic release events. When synapses were driven instead by double pulses, more representative of the bursty inputs that occur in vivo, we found that the tolerance for input desynchronization was increased by more than an order of magnitude. The effect depended mainly on paired pulse facilitation of NMDA receptor-mediated responses at Schaffer collateral synapses. Our results suggest that CA1 pyramidal cells could function as nonlinear integrative units in all major hippocampal states.
Skokos, Ch; Bodyfelt, J D; Papamikos, G; Eggl, S
2013-01-01
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not yet been studied in detail. We demonstrate ways to construct high order symplectic integrators for Hamiltonian systems that can be split in three integrable parts. Using these techniques for the integration of the disordered, discrete nonlinear Schroedinger equation, we show that three part split symplectic integrators are more efficient than other numerical methods for the long time integration of multidimensional systems, with respect to both accuracy and computational time.
Energy Technology Data Exchange (ETDEWEB)
Vakhnenko, Oleksiy O., E-mail: vakhnenko@bitp.kiev.ua
2016-05-27
Highlights: • The integrable nonlinear Schrödinger system on a triangular-lattice ribbon is inclined to metamorphoses. • The system under study is capable to incorporate the effect of external linear potential. • The system criticality against the background parameter reduces the number of independent field variables. • At critical point the system Poisson structure becomes degenerate. • The effect of criticality is elucidated by the system one-soliton solution. - Abstract: The variativity of governing coupling parameters in the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is shown to ensure the important qualitative rearrangements in the system dynamics. There are at least the two types of system crucial modifications stipulated by the two types of governing parameters. Thus the longitudinal coupling parameters regulated mainly by the background values of concomitant field variables are responsible for the bifurcation of primary integrable nonlinear system into the integrable nonlinear system of Ablowitz–Ladik type. As a consequence in a critical point the number of independent field variables is reduced by a half and the system Poisson structure turns out to be degenerate. On the other hand the transverse coupling parameters regulated basically by the choice of their a priori arbitrary dependencies on time are capable to incorporate the effect of external linear potential. As a consequence the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modeling the Bloch oscillations of charged nonlinear carriers in an electrically biased ribbon of triangular lattice. The multi-component structure of basic integrable system alongside with the attractive character of system nonlinearities has predetermined the logic of whole consideration.
Choi, Ho-Lim
2014-12-01
In this paper, we provide an output feedback solution over one given by Choi and Lim [Systems & Control Letters, 59(6), 374-379 (2010)] under more generalised system set-up. More specifically, we consider a stabilisation problem of a chain of integrators that has nonlinearity and an uncertain delay in the input by output feedback. The nonlinearity is classified into four types. Then, we propose a memoryless output feedback controller which contains a gain-scaling factor to adjust controller gains depending on the given nonlinearity type. Our stability analysis shows that the controlled system has unique stabilisation result associated with each type of nonlinearity. Our result provides a new aspect to the stabilisation problem of nonlinear time-delay systems and broadens the existing control results of time-delay systems. Two examples are given for illustration.
Energy Technology Data Exchange (ETDEWEB)
Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir [Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of); The Laboratory of Quantum Information Processing, Yazd University, Yazd (Iran, Islamic Republic of); Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir [Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of); The Laboratory of Quantum Information Processing, Yazd University, Yazd (Iran, Islamic Republic of); Cattani, C., E-mail: ccattani@unisa.it [Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (Italy); Maalek Ghaini, F.M., E-mail: maalek@yazd.ac.ir [Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of); The Laboratory of Quantum Information Processing, Yazd University, Yazd (Iran, Islamic Republic of)
2015-02-15
Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.
Liouvillian integrability of gravitating static isothermal fluid spheres
Iacono, Roberto; Llibre, Jaume
2014-10-01
We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka-Volterra quadratic polynomial differential system in {R}^2, and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka-Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka-Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.
Liouvillian integrability of gravitating static isothermal fluid spheres
Energy Technology Data Exchange (ETDEWEB)
Iacono, Roberto, E-mail: roberto.iacono@enea.it [ENEA-C. R. Casaccia, Via Anguillarese 301, 00123 Roma (Italy); Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia (Spain)
2014-10-01
We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka–Volterra quadratic polynomial differential system in R² and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka–Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka–Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.
Directory of Open Access Journals (Sweden)
Ahmad Molabahrami
2013-09-01
Full Text Available In this paper, the integral mean value method is employed to handle the general nonlinear Fredholm integro-differential equations under the mixed conditions. The application of the method is based on the integral mean value theorem for integrals. By using the integral mean value method, an integro-differential equation is transformed to an ordinary differential equation, then by solving it, the obtained solution is transformed to a system of nonlinear algebraic equations to calculate the unknown values. The efficiency of the approach will be shown by applying the procedure on some examples. In this respect, a comparison with series pattern solutions, obtained by some analytic methods, is given. For the approximate solution given by integral mean value method, the bounds of the absolute errors are given. The Mathematica program of the integral mean value method based on the procedure in this paper is designed.
Integrated nanoplasmonic waveguides for magnetic, nonlinear, and strong-field devices
Sederberg, Shawn; Firby, Curtis J.; Greig, Shawn R.; Elezzabi, Abdulhakem Y.
2017-01-01
As modern complementary-metal-oxide-semiconductor (CMOS) circuitry rapidly approaches fundamental speed and bandwidth limitations, optical platforms have become promising candidates to circumvent these limits and facilitate massive increases in computational power. To compete with high density CMOS circuitry, optical technology within the plasmonic regime is desirable, because of the sub-diffraction limited confinement of electromagnetic energy, large optical bandwidth, and ultrafast processing capabilities. As such, nanoplasmonic waveguides act as nanoscale conduits for optical signals, thereby forming the backbone of such a platform. In recent years, significant research interest has developed to uncover the fundamental physics governing phenomena occurring within nanoplasmonic waveguides, and to implement unique optical devices. In doing so, a wide variety of material properties have been exploited. CMOS-compatible materials facilitate passive plasmonic routing devices for directing the confined radiation. Magnetic materials facilitate time-reversal symmetry breaking, aiding in the development of nonreciprocal isolators or modulators. Additionally, strong confinement and enhancement of electric fields within such waveguides require the use of materials with high nonlinear coefficients to achieve increased nonlinear optical phenomenon in a nanoscale footprint. Furthermore, this enhancement and confinement of the fields facilitate the study of strong-field effects within the solid-state environment of the waveguide. Here, we review current state-of-the-art physics and applications of nanoplasmonic waveguides pertaining to passive, magnetoplasmonic, nonlinear, and strong-field devices. Such components are essential elements in integrated optical circuitry, and each fulfill specific roles in truly developing a chip-scale plasmonic computing architecture.
Global behavior of n-dimensional Lotka-Volterra systems.
Gouzé, J L
1993-02-01
The behavior of Lotka-Volterra systems is studied using as tools the results from positivity and auxiliary functions that decrease along the trajectories. One typical result is that if a decomposition of the interaction matrix into a product of a symmetric and an off-diagonal nonnegative matrix is possible, then all the trajectories either go to equilibria or cannot remain in any compact set of the interior of the positive orthant.
Crosscumulants Based Approaches for the Structure Identification of Volterra Models
Institute of Scientific and Technical Information of China (English)
Houda Mathlouthi; Kamel Abederrahim; Faouzi Msahli; Gerard Favier
2009-01-01
In this paper, we address the problem of structure identification of Volterra models. It consists in estimating the model order and the memory lcngth of each kernel. Two methods based on input-output crosscumulants arc developed. The first one uses zero mean independent and identically distributed Ganssian input, and the second one concerns a symmetric input sequence. Simulations are performed on six models having different orders and kernel memory lengths to demonstrate the advantages of the proposed methods.
Positive periodic solutions of delayed periodic Lotka-Volterra systems
Energy Technology Data Exchange (ETDEWEB)
Lin Wei [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: weilin@fudan.edu.cn; Chen Tianping [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: tchen@fudan.edu.cn
2005-01-17
In this Letter, for a general class of delayed periodic Lotka-Volterra systems, we prove some new results on the existence of positive periodic solutions by Schauder's fixed point theorem. The global asymptotical stability of positive periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.
A simple spatiotemporal chaotic Lotka-Volterra model
Energy Technology Data Exchange (ETDEWEB)
Sprott, J.C. [Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706 (United States)] e-mail: sprott@physics.wisc.edu; Wildenberg, J.C. [Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706 (United States)] e-mail: jcwildenberg@wisc.edu; Azizi, Yousef [Institute for Advanced Studies in Basic Sciences, Zanjan (Iran, Islamic Republic of)] e-mail: joseph_azizi@yahoo.com
2005-11-01
A mathematically simple example of a high-dimensional (many-species) Lotka-Volterra model that exhibits spatiotemporal chaos in one spatial dimension is described. The model consists of a closed ring of identical agents, each competing for fixed finite resources with two of its four nearest neighbors. The model is prototypical of more complicated models in its quasiperiodic route to chaos (including attracting 3-tori), bifurcations, spontaneous symmetry breaking, and spatial pattern formation.
Stability and monotonicity of Lotka-Volterra type operators
Mukhamedov, Farrukh
2009-01-01
In the present paper, we study Lotka-Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. After, we introduce a new class of LV-type operators, called $M$LV type. We prove convergence of their trajectories and study certain its properties. Moreover, we show that such kind of operators have totaly different behavior than ${\\mathbf{f}}$-monotone LV type operators.
Indian Academy of Sciences (India)
O S IYIOLA; F D ZAMAN
2016-10-01
In this paper, we consider the (2+1) nonlinear fractional heat equation with non-local integral terms and investigate two different cases of such non-local integral terms. The first has to do with the time-dependent non-local integral term and the second is the space-dependent non-local integral term. Apart from the nonlinear nature of these formulations, the complexity due to the presence of the non-local integral terms impelled us to use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the solutions obtained by this method.
Integration of a nonlinear energy sink and a giant magnetostrictive energy harvester
Fang, Zhi-Wei; Zhang, Ye-Wei; Li, Xiang; Ding, Hu; Chen, Li-Qun
2017-03-01
This paper explores a promising novel approach by integrating nonlinear energy sink (NES) and giant magnetostrictive material (GMM) to realize vibration control and energy harvesting. The vibration-based apparatus consisting of a NES, a Terfenol-D rod, and a linear oscillator (the primary system) is proposed. The mathematical model of the prototype under displacement driven has been established and simulated by utilizing the Runge-Kutta algorithm. The exhibited responses and the obtained electric energy are computed. Furthermore, the Fast Fourier Transform (FFT) of the resonant responses is performed. The distribution of the input energy is calculated to evaluate the designed structure. The instantaneous transaction of the energy is then examined by considering the energy transaction measure (ETM). Lastly, a parametric study is conducted for further optimization. The numerical simulations demonstrate that the nonlinear pumping phenomena occur, that is, the target energy transfer (TET) that leads to a very efficient vibration suppression. In addition, the results also illustrate that the localized vibration energy can be converted into magnetic field energy due to the Villari effect and then transformed into electric energy.
Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations
Guoqiang, Han; Jiong, Wang
2001-09-01
In this paper, we analyze the existence of asymptotic error expansion of the Nystrom solution for two-dimensional nonlinear Fredholm integral equations of the second kind. We show that the Nystrom solution admits an error expansion in powers of the step-size h and the step-size k. For a special choice of the numerical quadrature, the leading terms in the error expansion for the Nystrom solution contain only even powers of h and k, beginning with terms h2p and k2q. These expansions are useful for the application of Richardson extrapolation and for obtaining sharper error bounds. Numerical examples show that how Richardson extrapolation gives a remarkable increase of precision, in addition to faster convergence.
Effective integration of ultra-elliptic solutions of the focusing nonlinear Schrödinger equation
Wright, O. C.
2016-05-01
An effective integration method based on the classical solution of the Jacobi inversion problem, using Kleinian ultra-elliptic functions and Riemann theta functions, is presented for the quasi-periodic two-phase solutions of the focusing cubic nonlinear Schrödinger equation. Each two-phase solution with real quasi-periods forms a two-real-dimensional torus, modulo a circle of complex-phase factors, expressed as a ratio of theta functions associated with the Riemann surface of the invariant spectral curve. The initial conditions of the Dirichlet eigenvalues satisfy reality conditions which are explicitly parametrized by two physically-meaningful real variables: the squared modulus and a scalar multiple of the wavenumber. Simple new formulas for the maximum modulus and the minimum modulus are obtained in terms of the imaginary parts of the branch points of the Riemann surface.
Non-Linear Integral Equations for complex Affine Toda associated to simply laced Lie algebras
Zinn-Justin, P
1998-01-01
A set of coupled non-linear integral equations is derived for a class of models connected with the quantum group $U_q(\\hat g)$ ($q=e^{i\\gamma}$ and $g$ simply laced Lie algebra), which are solvable using the Bethe Ansatz; these equations describe arbitrary excited states of a system with finite spatial length $L$. They generalize the Destri-De Vega equation for the Sine-Gordon/massive Thirring model to affine Toda field theory with imaginary coupling constant. As an application, the central charge and all the conformal weights of the UV conformal field theory are extracted in a straightforward manner. The quantum group truncation for rational values of $\\gamma/\\pi$ is discussed in detail; in the UV limit we recover through this procedure the RCFTs with extended $W(g)$ conformal symmetry.
Chai, Zhen; Hu, Xiaoyong; Yang, Hong; Gong, Qihuang
2017-01-01
Ultracompact chip-integrated all-optical diode is realized experimentally in a plasmonic microstructure, consisting of a plasmonic waveguide side-coupled two asymmetric plasmonic composite nanocavities covered with a multicomponent nanocomposite layer, formed directly in a plasmonic circuit. Extremely large optical nonlinearity enhancement is obtained for the multicomponent nanocomposite cover layer, originating from resonant excitation, slow-light effect, and field enhancement effect. Nonreciprocal transmission was achieved based on the difference in the shift magnitude of the transparency window centers of two asymmetric plasmonic nanocavities induced by the signal light, itself, for the forward and backward propagation cases. An ultralow threshold incident light power of 145 μW (corresponding to a threshold intensity of 570 kW/cm2) is realized, which is reduced by seven orders of magnitude compared with previous reports. An ultrasmall feature size of 2 μm and a transmission contrast ratio of 15 dB are obtained simultaneously.
Volterra prediction model for speech signal series%语音信号序列的Volterra预测模型∗
Institute of Scientific and Technical Information of China (English)
张玉梅; 胡小俊; 吴晓军; 白树林; 路纲
2015-01-01
The given English phonemes, words and sentences are sampled and preprocessed. For these real measured speech signal series, time delay and embedding dimension are determined by using mutual information method and Cao’s method, respectively, so as to perform phase space reconstruction of the speech signal series. By using small data set method, the largest Lyapunov exponent of the speech signal series is calculated and the fact that its value is greater than zero presents chaotic characteristics of the speech signal series. This, in fact, performs the chaotic characteristic identification of the speech signal series. By introducing second-order Volterra series, in this paper we put forward a type of nonlinear prediction model with an explicit structure. To overcome some intrinsic shortcomings caused by improper parameter selection when using the least mean square (LMS) algorithm to update Volterra model eﬃciency, by using a variable convergence factor technology based on a posteriori error assumption on the basis of LMS algorithm, a novel Davidon-Fletcher-Powell-based second of Volterra filter (DFPSOVF) is constructed and is performed to predict speech signal series of the given English phonemes, words and sentences with chaotic characteristics. Simulation results under MATLAB 7.0 environment show that the proposed nonlinear model DFPSOVF can guarantee its stability and convergence and there are no divergence problems in using LMS algorithm; for single-frame and multi-frame of the measured speech signals, when root mean square error (RMSE) is used as an evaluation criterion the prediction accuracy of the proposed nonlinear prediction model DFPSOVF in this paper is better than that of the linear prediction (LP) that is traditionally employed. The primary results of single-frame and multi-frame predictions are given. So, the proposed DFPSOVF model can substitute linear prediction model on certain conditions. Meanwhile, it can better reflect trends and regularity
Application of homotopy-perturbation method to nonlinear population dynamics models
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, M.S.H. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia); Hashim, I. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)], E-mail: ishak_h@ukm.my; Abdulaziz, O. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)
2007-08-20
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)
Rational Expansion for Nonlinear Input-Output Maps
1988-01-01
This paper introduces a Rational Expansion for Nonlinear Input-Output MAPS. The method is new and is based on the rational expansion of functions of several complex variables. If truncated, this series reduces to a ratio of truncated Volterra series, A "feedback form" will be presented.
Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations
Directory of Open Access Journals (Sweden)
H.L. Tidke
2010-12-01
Full Text Available The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.
Analytic solutions of a class of nonlinearly dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Wang, M-C [System Engineering Institute of Tianjin University, Tianjin, 300072 (China); Zhao, X-S; Liu, X [Tianjin University of Technology and Education, Tianjin, 300222 (China)], E-mail: mchwang123@163.com.cn, E-mail: xszhao@mail.nwpu.edu.cn, E-mail: liuxinhubei@163.com.cn
2008-02-15
In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently.
Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources
Directory of Open Access Journals (Sweden)
Aurel A Lazar
2014-09-01
Full Text Available We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a nonlinear dendritic stimulus processor (DSP cascaded with a biophysical spike generator (BSG. The nonlinear dendritic processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits.We investigate two intrinsic noise sources arising (i in the active dendritic trees underlying the DSPs, and (ii in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements.For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.
DEFF Research Database (Denmark)
Jimenez, M.J.; Madsen, Henrik; Bloem, J.J.
2008-01-01
(MAP) estimation is presented along with a software implementation. As a case study, the modelling of the thermal characteristics of a building integrated PV component is considered. The EC-JRC Ispra has made experimental data available. Both linear and non-linear models are identified. It is shown...
Bi-Hamiltonian systems and Lotka-Volterra equations: A three dimensional classification
Plank, Manfred
1995-01-01
We study three dimensional bi-Hamiltonian systems in general and use the obtained results to classify all three dimensional Lotka-Volterra equations, which admit a bi-Hamiltonian representation. In der vorliegenden Arbeit studieren wir drei-dimensionale bi-Hamiltonsche Systeme und klassifizieren alle drei-dimensionalen Lotka-Volterra Gleichungen, welche eine bi-Hamiltonsche Darstellung zulassen.
Robust Integral of Neural Network and Error Sign Control of MIMO Nonlinear Systems.
Yang, Qinmin; Jagannathan, Sarangapani; Sun, Youxian
2015-12-01
This paper presents a novel state-feedback control scheme for the tracking control of a class of multi-input multioutput continuous-time nonlinear systems with unknown dynamics and bounded disturbances. First, the control law consisting of the robust integral of a neural network (NN) output plus sign of the tracking error feedback multiplied with an adaptive gain is introduced. The NN in the control law learns the system dynamics in an online manner, while the NN residual reconstruction errors and the bounded disturbances are overcome by the error sign signal. Since both of the NN output and the error sign signal are included in the integral, the continuity of the control input is ensured. The controller structure and the NN weight update law are novel in contrast with the previous effort, and the semiglobal asymptotic tracking performance is still guaranteed by using the Lyapunov analysis. In addition, the NN weights and all other signals are proved to be bounded simultaneously. The proposed approach also relaxes the need for the upper bounds of certain terms, which are usually required in the previous designs. Finally, the theoretical results are substantiated with simulations.
Integrable Nonlinear Schrödinger System on a Triangular-Lattice Ribbon
Vakhnenko, Oleksiy O.
2015-01-01
An integrable nonlinear Schrödinger system on a triangular-lattice ribbon, whose geometric configuration is similar to that of (1,1) armchair boron nanotube, is studied in detail. The system Hamiltonian formulation is shown to underline an essentially nontrivial Poisson structure associated with four basic field variables appearing as nearly amplitudes of the probability to find the lattice sites being excited and with two concomitant field variables maintaining the finite background. The coupling parameters of the system are allowed to be complex-valued ones thus permitting to model external magnetic fluxes threading the elementary plackets of a lattice in terms of Peierls phases. An alternative version of zero-curvature representation given in terms of 2 × 2 auxiliary spectral and evolution matrices is proved to support the constructive integrability of the system by means of Darboux-Bäcklund dressing method. In the framework of Darboux approach the one-soliton solution is found explicitly and analyzed with special attention to the principal differences between the bare and physical soliton parameters.
Institute of Scientific and Technical Information of China (English)
娄梅枝
2003-01-01
In this paper, A.B.Mingarelli's result is generalized to General Volterra-Stieltjes Integro-differential Equations. Comparison theorem and equivalence condition of non-oscillation are obtained. Classical Sturm comparison theorem and some conclusions are generalized.
DEFF Research Database (Denmark)
Chon, K H; Cohen, R J; Holstein-Rathlou, N H
1997-01-01
A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving...... average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre...... function remain with our algorithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of Laguerre functions can be made, compared with the Volterra-Wiener approach. This translates into a more compact system representation and makes...
Global topological classification of Lotka-Volterra quadratic differential systems
Directory of Open Access Journals (Sweden)
Dana Schlomiuk
2012-04-01
Full Text Available The Lotka-Volterra planar quadratic differential systems have numerous applications but the global study of this class proved to be a challenge difficult to handle. Indeed, the four attempts to classify them (Reyn (1987, W"orz-Buserkros (1993, Georgescu (2007 and Cao and Jiang (2008 produced results which are not in agreement. The lack of adequate global classification tools for the large number of phase portraits encountered, explains this situation. All Lotka-Volterra systems possess invariant straight lines, each with its own multiplicity. In this article we use as a global classification tool for Lotka-Volterra systems the concept of configuration of invariant lines (including the line at infinity. The class splits according to the types of configurations in smaller subclasses which makes it easier to have a good control over the phase portraits in each subclass. At the same time the classification becomes more transparent and easier to grasp. We obtain a total of 112 topologically distinct phase portraits: 60 of them with exactly three invariant lines, all simple; 27 portraits with invariant lines with total multiplicity at least four; 5 with the line at infinity filled up with singularities; 20 phase portraits of degenerate systems. We also make a thorough analysis of the results in the paper of Cao and Jiang [13]. In contrast to the results on the classification in [13], done in terms of inequalities on the coefficients of normal forms, we construct invariant criteria for distinguishing these portraits in the whole parameter space $mathbb{R}^{12}$ of coefficients.
Statistics of extinction and survival in Lotka-Volterra systems
Abramson, G; Abramson, Guillermo; Zanette, Damian
1998-01-01
We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the number of surviving species depends strongly on the statistical properties of the interaction matrix, and that the probability of survival is weakly correlated to specific initial conditions.
String networks in ZN Lotka-Volterra competition models
Avelino, P. P.; Bazeia, D.; Menezes, J.; de Oliveira, B. F.
2014-01-01
In this Letter we give specific examples of ZN Lotka-Volterra competition models leading to the formation of string networks. We show that, in order to promote coexistence, the species may arrange themselves around regions with a high number density of empty sites generated by predator-prey interactions between competing species. These configurations extend into the third dimension giving rise to string networks. We investigate the corresponding dynamics using both stochastic and mean field theory simulations, showing that the coarsening of these string networks follows a scaling law which is analogous to that found in other physical systems in condensed matter and cosmology.
Coexistence and Survival in Conservative Lotka-Volterra Networks
Knebel, Johannes; Krüger, Torben; Weber, Markus F.; Frey, Erwin
2013-04-01
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network’s interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.
Coexistence and survival in conservative Lotka-Volterra networks.
Knebel, Johannes; Krüger, Torben; Weber, Markus F; Frey, Erwin
2013-04-19
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.
Species clustering in competitive Lotka-Volterra models.
Pigolotti, Simone; López, Cristóbal; Hernández-García, Emilio
2007-06-22
We study the properties of general Lotka-Volterra models with competitive interactions. The intensity of the competition depends on the position of species in an abstract niche space through an interaction kernel. We show analytically and numerically that the properties of these models change dramatically when the Fourier transform of this kernel is not positive definite, due to a pattern-forming instability. We estimate properties of the species distributions, such as the steady number of species and their spacings, for different types of interactions, including stretched exponential and constant kernels.
Extinction dynamics of Lotka-Volterra ecosystems on evolving networks.
Coppex, F; Droz, M; Lipowski, A
2004-06-01
We study a model of a multispecies ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law distribution of intervals between extinctions, but only for ecosystems with sufficient variability of species and with networks of connectivity above certain threshold that is very close to the percolation threshold of the network. The effect of slow environmental changes on extinction dynamics, degree distribution of the network of interspecies interactions, and some emergent properties of our model are also examined.
Free Boundary Problems for a Lotka-Volterra Competition System
Wang, Mingxin; Zhao, Jingfu
2014-09-01
In this paper we investigate two free boundary problems for a Lotka-Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free boundary. We prove a spreading-vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of the solutions and criteria for spreading and vanishing are also obtained. This paper is an improvement and extension of J. Guo and C. Wu.
Winnerless competition in coupled Lotka-Volterra maps.
González-Díaz, L A; Gutiérrez, E D; Varona, P; Cabrera, J L
2013-07-01
Winnerless competition is analyzed in coupled maps with discrete temporal evolution of the Lotka-Volterra type of arbitrary dimension. Necessary and sufficient conditions for the appearance of structurally stable heteroclinic cycles as a function of the model parameters are deduced. It is shown that under such conditions winnerless competition dynamics is fully exhibited. Based on these conditions different cases characterizing low, intermediate, and high dimensions are therefore computationally recreated. An analytical expression for the residence times valid in the N-dimensional case is deduced and successfully compared with the simulations.
The Quench Map in an Integrable Classical Field Theory: Nonlinear Schr\\"odinger Equation
Caudrelier, Vincent
2016-01-01
We study the non-equilibrium dynamics obtained by an abrupt change (a {\\em quench}) in the parameters of an integrable classical field theory, the nonlinear Schr\\"odinger equation. We first consider explicit one-soliton examples, which we fully describe by solving the direct part of the inverse scattering problem. We then develop some aspects of the general theory using elements of the inverse scattering method. For this purpose, we introduce the {\\em quench map} which acts on the space of scattering data and represents the change of parameter with fixed field configuration (initial condition). We describe some of its analytic properties by implementing a higher level version of the inverse scattering method, and we discuss the applications of Darboux-B\\"acklund transformations, Gelfand-Levitan-Marchenko equations and the Rosales series solution to a related, dual quench problem. Finally, we comment on the interplay between quantum and classical tools around the theme of quenches and on the usefulness of the ...
The quench map in an integrable classical field theory: nonlinear Schrödinger equation
Caudrelier, Vincent; Doyon, Benjamin
2016-11-01
We study the non-equilibrium dynamics obtained by an abrupt change (a quench) in the parameters of an integrable classical field theory, the nonlinear Schrödinger equation. We first consider explicit one-soliton examples, which we fully describe by solving the direct part of the inverse scattering problem. We then develop some aspects of the general theory using elements of the inverse scattering method. For this purpose, we introduce the quench map which acts on the space of scattering data and represents the change of parameter with fixed field configuration (initial condition). We describe some of its analytic properties by implementing a higher level version of the inverse scattering method, and we discuss the applications of Darboux–Bäcklund transformations, Gelfand–Levitan–Marchenko equations and the Rosales series solution to a related, dual quench problem. Finally, we comment on the interplay between quantum and classical tools around the theme of quenches and on the usefulness of the quantization of our classical approach to the quantum quench problem.
Liu, Yan-Jun; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan
2016-09-19
A neural network (NN) adaptive control design problem is addressed for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. The considered systems contain uncertainty dynamics and their states are enforced to subject to bounded constraints as well as the couplings among various inputs and outputs are inserted in each subsystem. To stabilize this class of systems, a novel adaptive control strategy is constructively framed by using the backstepping design technique and NNs. The novel integral barrier Lyapunov functionals (BLFs) are employed to overcome the violation of the full state constraints. The proposed strategy can not only guarantee the boundedness of the closed-loop system and the outputs are driven to follow the reference signals, but also can ensure all the states to remain in the predefined compact sets. Moreover, the transformed constraints on the errors are used in the previous BLF, and accordingly it is required to determine clearly the bounds of the virtual controllers. Thus, it can relax the conservative limitations in the traditional BLF-based controls for the full state constraints. This conservatism can be solved in this paper and it is for the first time to control this class of MIMO systems with the full state constraints. The performance of the proposed control strategy can be verified through a simulation example.
Bayesian integration and non-linear feedback control in a full-body motor task.
Directory of Open Access Journals (Sweden)
Ian H Stevenson
2009-12-01
Full Text Available A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller. We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.
Positive periodic solutions of periodic neutral Lotka-Volterra system with distributed delays
Energy Technology Data Exchange (ETDEWEB)
Li Yongkun [Department of Mathematics, Yunnan University Kunming, Yunnan 650091 (China)], E-mail: yklie@ynu.edu.cn
2008-07-15
By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka-Volterra system with distributed delays (dx{sub i}(t))/(dt) =x{sub i}(t)[a{sub i}(t)-{sigma}{sub j=1}{sup n}b{sub ij}(t){integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})x{sub j}( t+{theta})d{theta}-{sigma}{sub j=1}{sup n}c{sub ij}(t){integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta}) x{sub j}{sup '}(t+{theta})d{theta}],i=1,2,...,n, where a{sub i},b{sub ij},c{sub ij} element of C(R,R{sup +}) (i, j = 1, 2, ..., n) are {omega}-periodic functions, T{sub ij},T{sub ij} element of (0,{infinity}) (i, j = 1, 2, ..., n) and K{sub ij},K{sub ij} element of (R,R{sup +}) satisfying {integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})d{theta}=1,{integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})d{theta}=1, i, j = 1, 2, ..., n.
Nonlinear resonance in Dufﬁng oscillator with ﬁxed and integrative time-delayed feedbacks
Indian Academy of Sciences (India)
V Ravichandran; V Chinnathambi; S Rajasekar
2012-03-01
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 time-delayed feedback. Applying the perturbation theory we obtain a nonlinear equation for the amplitude of the periodic response of the system. For a range of values of and , the response amplitude is found to be higher than that of the system in the absence of delayed feedback. The response amplitude is periodic on the parameter with period 2 / where is the angular frequency of the external periodic force. We show the occurrence of multiple branches of the response amplitude curve with and without hysteresis.
Indian Academy of Sciences (India)
EMRULLAH YA¸SAR; YAKUP YILDIRIM; ILKER BURAK GIRESUNLU
2016-08-01
Fin materials can be observed in a variety of engineering applications. They are used to ease the dissipation of heat from a heated wall to the surrounding environment. In this work, we consider a nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. The equation(s) under study are highly nonlinear. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. Firstly, we consider the Lie group analysis for different cases of thermal conductivity and the heat transfer coefficients. These classifications are obtained from the Lie group analysis. Then, the first integrals of the nonlinear straight fin problem are constructed by three methods, namely, Noether’s classical method, partial Noether approach and Ibragimov’s nonlocal conservation method. Some exact analytical solutions are also constructed. The obtained result is also compared with the result obtained by other methods.
Energy Technology Data Exchange (ETDEWEB)
Xie, G.; Li, J.; Majer, E.; Zuo, D.
1998-07-01
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
Modal Identification Using OMA Techniques: Nonlinearity Effect
Directory of Open Access Journals (Sweden)
E. Zhang
2015-01-01
Full Text Available This paper is focused on an assessment of the state of the art of operational modal analysis (OMA methodologies in estimating modal parameters from output responses of nonlinear structures. By means of the Volterra series, the nonlinear structure excited by random excitation is modeled as best linear approximation plus a term representing nonlinear distortions. As the nonlinear distortions are of stochastic nature and thus indistinguishable from the measurement noise, a protocol based on the use of the random phase multisine is proposed to reveal the accuracy and robustness of the linear OMA technique in the presence of the system nonlinearity. Several frequency- and time-domain based OMA techniques are examined for the modal identification of simulated and real nonlinear mechanical systems. Theoretical analyses are also provided to understand how the system nonlinearity degrades the performance of the OMA algorithms.
An integrating factor matrix method to find first integrals
Energy Technology Data Exchange (ETDEWEB)
Saputra, K V I [Faculty of Science and Mathematics, University Pelita Harapan, Jl. MH Thamrin Boulevard, Tangerang Banten, 15811 (Indonesia); Quispel, G R W [Department of Mathematics and Statistical Science, La Trobe University, Bundoora 3086 (Australia); Van Veen, L, E-mail: kie.saputra@staff.uph.ed [Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe St N., Oshawa, Ontario, L1H 7K4 (Canada)
2010-06-04
In this paper we develop an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along with the conditions for their existence, for two- and three-dimensional Lotka-Volterra systems with constant terms. The results are compared to previous results obtained by other methods.
An integrating factor matrix method to find first integrals
Saputra, K V I; van Veen, L
2010-01-01
In this paper we developed an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along with the conditions for their existence, for two and three dimensional Lotka-Volterra systems with constant terms. The results are compared to previous results obtained by other methods.
A reduced-rank approach for implementing higher-order Volterra filters
O. Batista, Eduardo L.; Seara, Rui
2016-12-01
The use of Volterra filters in practical applications is often limited by their high computational burden. To cope with this problem, many strategies for implementing Volterra filters with reduced complexity have been proposed in the open literature. Some of these strategies are based on reduced-rank approaches obtained by defining a matrix of filter coefficients and applying the singular value decomposition to such a matrix. Then, discarding the smaller singular values, effective reduced-complexity Volterra implementations can be obtained. The application of this type of approach to higher-order Volterra filters (considering orders greater than 2) is however not straightforward, which is especially due to some difficulties encountered in the definition of higher-order coefficient matrices. In this context, the present paper is devoted to the development of a novel reduced-rank approach for implementing higher-order Volterra filters. Such an approach is based on a new form of Volterra kernel implementation that allows decomposing higher-order kernels into structures composed only of second-order kernels. Then, applying the singular value decomposition to the coefficient matrices of these second-order kernels, effective implementations for higher-order Volterra filters can be obtained. Simulation results are presented aiming to assess the effectiveness of the proposed approach.
Merkel, Philipp
2012-01-01
In this paper, we recompute contributions to the spectrum of the nonlinear integrated Sachs-Wolfe (iSW)/Rees-Sciama effect in a dark energy cosmology. Focusing on the moderate nonlinear regime, all dynamical fields involved are derived from the density contrast in Eulerian perturbation theory. Shape and amplitude of the resulting angular power spectrum are similar to that derived in previous work. With our purely analytical approach we identify two distinct contributions to the signal of the nonlinear iSW-effect: the change of the gravitational self-energy density of the large scale structure with (conformal) time and gravitational lenses moving with the large scale matter stream. In the latter we recover the Birkinshaw-Gull effect. As the nonlinear iSW-effect itself is inherently hard to detect, observational discrimination between its individual contributions is almost excluded. Our analysis, however, yields valuable insights into the theory of the nonlinear iSW-effect as a post-Newtonian relativistic effec...
Lotka-Volterra competition models for sessile organisms.
Spencer, Matthew; Tanner, Jason E
2008-04-01
Markov models are widely used to describe the dynamics of communities of sessile organisms, because they are easily fitted to field data and provide a rich set of analytical tools. In typical ecological applications, at any point in time, each point in space is in one of a finite set of states (e.g., species, empty space). The models aim to describe the probabilities of transitions between states. In most Markov models for communities, these transition probabilities are assumed to be independent of state abundances. This assumption is often suspected to be false and is rarely justified explicitly. Here, we start with simple assumptions about the interactions among sessile organisms and derive a model in which transition probabilities depend on the abundance of destination states. This model is formulated in continuous time and is equivalent to a Lotka-Volterra competition model. We fit this model and a variety of alternatives in which transition probabilities do not depend on state abundances to a long-term coral reef data set. The Lotka-Volterra model describes the data much better than all models we consider other than a saturated model (a model with a separate parameter for each transition at each time interval, which by definition fits the data perfectly). Our approach provides a basis for further development of stochastic models of sessile communities, and many of the methods we use are relevant to other types of community. We discuss possible extensions to spatially explicit models.
Population dynamics and wave propagation in a Lotka-Volterra system with spatial diffusion
Wang, Mao-Xiang; Lai, Pik-Yin
2012-11-01
We consider the competitive population dynamics of two species described by the Lotka-Volterra model in the presence of spatial diffusion. The model is described by the diffusion coefficient (dα) and proliferation rate (rα) of the species α (α=1,2 is the species label). Propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. It is found that the wave profiles and wave speeds are determined by the speed parameters, vα≡2dαrα, of the two species, and the phase diagrams for various inter- and intracompetitive scenarios are determined. The steady wave front speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. The effect of the intermediate stationary state is investigated and propagating wave profiles beyond the simple Fisher wave fronts are revealed. The wave front speed of a species can display abrupt increase as its speed parameter is increased. In particular for the case in which both species are aggressive, our results show that the speed parameter is the deciding factor that determines the ultimate surviving species, in contrast to the case without diffusion in which the final surviving species is decided by its initial population advantage. Possible relations to the biological relevance of modeling cancer development and wound healing are also discussed.
Population dynamics and wave propagation in a Lotka-Volterra system with spatial diffusion.
Wang, Mao-Xiang; Lai, Pik-Yin
2012-11-01
We consider the competitive population dynamics of two species described by the Lotka-Volterra model in the presence of spatial diffusion. The model is described by the diffusion coefficient (d(α)) and proliferation rate (r(α)) of the species α (α = 1,2 is the species label). Propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. It is found that the wave profiles and wave speeds are determined by the speed parameters, v(α) ≡ 2 sqrt [d(α)r(α)], of the two species, and the phase diagrams for various inter- and intracompetitive scenarios are determined. The steady wave front speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. The effect of the intermediate stationary state is investigated and propagating wave profiles beyond the simple Fisher wave fronts are revealed. The wave front speed of a species can display abrupt increase as its speed parameter is increased. In particular for the case in which both species are aggressive, our results show that the speed parameter is the deciding factor that determines the ultimate surviving species, in contrast to the case without diffusion in which the final surviving species is decided by its initial population advantage. Possible relations to the biological relevance of modeling cancer development and wound healing are also discussed.
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
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S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
An equivalent condition for stability properties of Lotka-Volterra systems
Energy Technology Data Exchange (ETDEWEB)
Chu Tianguang [Intelligent Control Laboratory, Center for Systems and Control, School of Engineering, Peking University, Beijing 100871 (China)], E-mail: chutg@pku.edu.cn
2007-08-20
We give a solvable Lie algebraic condition for the equivalence of four typical stability notions (asymptotic stability, D-stability, total stability, and Volterra-Lyapunov stability) concerning Lotka-Volterra systems. Our approach makes use of the decomposition of the interaction matrix into symmetric and skew-symmetric parts, which may be related to the cooperative and competitive interaction pattern of a Lotka-Volterra system. The present result covers a known condition and can yield a larger set of interaction matrices for equivalence of the stability properties.
Indian Academy of Sciences (India)
Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang
2010-01-01
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
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Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
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Sharad Shandilya
Full Text Available The timing of defibrillation is mostly at arbitrary intervals during cardio-pulmonary resuscitation (CPR, rather than during intervals when the out-of-hospital cardiac arrest (OOH-CA patient is physiologically primed for successful countershock. Interruptions to CPR may negatively impact defibrillation success. Multiple defibrillations can be associated with decreased post-resuscitation myocardial function. We hypothesize that a more complete picture of the cardiovascular system can be gained through non-linear dynamics and integration of multiple physiologic measures from biomedical signals.Retrospective analysis of 153 anonymized OOH-CA patients who received at least one defibrillation for ventricular fibrillation (VF was undertaken. A machine learning model, termed Multiple Domain Integrative (MDI model, was developed to predict defibrillation success. We explore the rationale for non-linear dynamics and statistically validate heuristics involved in feature extraction for model development. Performance of MDI is then compared to the amplitude spectrum area (AMSA technique.358 defibrillations were evaluated (218 unsuccessful and 140 successful. Non-linear properties (Lyapunov exponent > 0 of the ECG signals indicate a chaotic nature and validate the use of novel non-linear dynamic methods for feature extraction. Classification using MDI yielded ROC-AUC of 83.2% and accuracy of 78.8%, for the model built with ECG data only. Utilizing 10-fold cross-validation, at 80% specificity level, MDI (74% sensitivity outperformed AMSA (53.6% sensitivity. At 90% specificity level, MDI had 68.4% sensitivity while AMSA had 43.3% sensitivity. Integrating available end-tidal carbon dioxide features into MDI, for the available 48 defibrillations, boosted ROC-AUC to 93.8% and accuracy to 83.3% at 80% sensitivity.At clinically relevant sensitivity thresholds, the MDI provides improved performance as compared to AMSA, yielding fewer unsuccessful defibrillations
Steen-Ermakov-Pinney equation and integrable nonlinear deformation of one-dimensional Dirac equation
Prykarpatskyy, Yarema
2017-01-01
The paper deals with nonlinear one-dimensional Dirac equation. We describe its invariants set by means of the deformed linear Dirac equation, using the fact that two ordinary differential equations are equivalent if their sets of invariants coincide.
The World According to Malthus and Volterra: The Mathematical Theory of the Struggle for Existence.
Bogdanov, Constantine
1992-01-01
Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)
Stochastic Volterra Equation Driven by Wiener Process and Fractional Brownian Motion
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Zhi Wang
2013-01-01
Full Text Available For a mixed stochastic Volterra equation driven by Wiener process and fractional Brownian motion with Hurst parameter H>1/2, we prove an existence and uniqueness result for this equation under suitable assumptions.
Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang
2015-06-01
Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.
Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays
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Ahmadjan Muhammadhaji
2015-01-01
Full Text Available We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.
Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system
Cherniha, Roman
2010-01-01
Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ans\\"atze to reduce the classical Lotka-Volterra systems with correctly-specified coefficients to ODE systems and examples of new exact solutions are found. A possible biological interpretation of some exact solutions is presented.
Food Web Assembly Rules for Generalized Lotka-Volterra Equations
DEFF Research Database (Denmark)
Härter, Jan Olaf Mirko; Mitarai, Namiko; Sneppen, Kim
2016-01-01
apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help......In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show...... that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify...
Verhulst-Lotka-Volterra (VLV) model of ideological struggles
Ausloos, Marcel R; Dimitrova, Zlatinka I
2011-01-01
Let the population of e.g. a country where some opinion struggle occurs be varying in time, according to Verhulst equation. Consider next some competition between opinions such as the dynamics be described by Lotka and Volterra equations. Two kinds of influences can be used, in such a model, for describing the dynamics of an agent opinion conversion: this can occur (i) either by means of mass communication tools, under some external field influence, or (ii) by means of direct interactions between agents. It results, among other features, that change(s) in environmental conditions can prevent the extinction of populations of followers of some ideology due to different kinds of resurrection effects. The tension arising in the country population is proposed to be measured by an appropriately defined scale index.
Computational Stability Analysis of Lotka-Volterra Systems
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Polcz Péter
2016-12-01
Full Text Available This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4 dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.
Stochastic analysis of the Lotka-Volterra model for ecosystems.
Cai, G Q; Lin, Y K
2004-10-01
A stochastic Lotka-Volterra-type model for the interaction between the preys and the predators in a random environment is investigated. A self-competition mechanism within the prey population itself is also included. The effect of a random environment is modeled as random variations in the birth rate of the preys and the death rate of the predators. The stochastic averaging procedure of Stratonovich and Khasminskii is applied to obtain the probability distributions of the system state variables at the state of statistical stationarity. Asymptotic behaviors of the system variables are discussed, and the mean transition time from an initial state to a critical state is obtained. Effects on the ecosystem behaviors of the self-competition term, of the random variation in the prey birth rate, and of the random variation in the predator death rate are investigated.
Nonextensivity of the cyclic lattice Lotka-Volterra model.
Tsekouras, G A; Provata, A; Tsallis, C
2004-01-01
We numerically show that the lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a finite production, per unit time, of the nonextensive entropy S(q)=(1- summation operator (i)p(q)(i))/(q-1) (S(1)=- summation operator (i)p(i) ln p(i)). This finiteness only occurs for q=0.5 for the d=2 growth mode (growing droplet), and for q=0 for the d=1 one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is, to our knowledge, exhibited for the first time for a many-body system which, at the mean field level, is conservative.
Conditions for Eltonian Pyramids in Lotka-Volterra Food Chains.
Jonsson, Tomas
2017-09-07
In ecological communities consumers (excluding parasites and parasitoids) are in general larger and less numerous than their resource. This results in a well-known observation known as 'Eltonian pyramids' or the 'pyramid of numbers', and metabolic arguments suggest that this pattern is independent of the number of trophic levels in a system. At the same time, Lotka-Volterra (LV) consumer-resource models are a frequently used tool to study many questions in community ecology, but their capacity to produce Eltonian pyramids has not been formally analysed. Here, I address this knowledge gap by investigating if and when LV food chain models give rise to Eltonian pyramids. I show that Eltonian pyramids are difficult to reproduce without density-dependent mortality in the consumers, unless biologically plausible relationships between mortality rate and interaction strength are taken into account.
The periodic competing Lotka-Volterra model with impulsive effect.
Liu, Bing; Chen, Lansun
2004-06-01
In this paper, the dynamic behaviour of a classical periodic Lotka-Volterra competing system with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equations, some conditions are obtained for the linear stability of the trivial and semi-trivial periodic solutions. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi-trivial periodic solution. As an application, a fish harvest problem is considered. We explain how two competing species, one of which in a periodic environment without impulsive effect would be doomed to extinction, can coexist with suitably periodic impulsive harvesting.
On solitary patterns in Lotka-Volterra chains
Zilburg, Alon; Rosenau, Philip
2016-03-01
We present and study a class of Lotka-Volterra chains with symmetric 2N-neighbors interactions. To identify the types of solitary waves which may propagate along the chain, we study their quasi-continuum approximations which, depending on the coupling between neighbors, reduce into a large variety of partial differential equations. Notable among the emerging equations is a bi-cubic equation {u}t={[{{bu}}2+2κ {{uu}}{xx}+{({u}{xx})}2]}x which we study in some detail. It begets remarkably stable topological and non-topological solitary compactons that interact almost elastically. They are used to identify discretons, their solitary discrete antecedents on the lattice, which decay at a doubly exponential rate. Many of the discrete modes are robust while others either decompose or evolve into breathers.
Complex Features in Lotka-Volterra Systems with Behavioral Adaptation
Tebaldi, Claudio; Lacitignola, Deborah
Lotka-Volterra systems have played a fundamental role for mathematical modelling in many branches of theoretical biology and proved to describe, at least qualitatively, the essential features of many phenomena, see for example Murray [Murray 2002]. Furthermore models of that kind have been considered successfully also in quite different and less mathematically formalized context: Goodwin' s model of economic growth cycles [Goodwin 1967] and urban dynamics [Dendrinos 1992] are only two of a number of examples. Such systems can certainly be defined as complex ones and in fact the aim of modelling was essentially to clarify mechanims rather than to provide actual precise simulations and predictions. With regards to complex systems, we recall that one of their main feature, no matter of the specific definition one has in mind, is adaptation, i. e. the ability to adjust.
El testamento y otros documentos sobre Daniele da Volterra
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Redín, Gonzalo
2010-09-01
Full Text Available Daniele da Volterra is better known in Spain for painting the drapery that covers some of the nudes in Michelangelo’s The Last Judgment than for his own work, which defined him as his master’s most loyal successor. Nonetheless, Daniele’s influence on Spanish art through Gaspar Becerra, a disciple of his in Rome, determined to a large extent the development of sculpture in this country in the second half of the 16th century. This article makes known and discusses Daniele’s previously unpublished last will and testament, located in the Archivio di Stato di Roma among the volumes by the notary Thomassino, who attended to the inventory of his possessions. It also provides new details on Daniele’s estate and on his direct disciples Michele Alberti, Feliciano de San Vito, and Biagio Betti along with his indirect ones such as Jacopo Rocchetti.
Daniele da Volterra es más conocido en España por pintar los paños que cubren algunos de los desnudos del Juicio final de Miguel Ángel, que por su obra, que le define como el más fiel heredero de su maestro. Sin embargo, su influencia en el arte español a través de Gaspar Becerra, discípulo suyo en Roma, condicionó el desarrollo de la escultura en buena parte de nuestro país en la segunda mitad del siglo XVI. Publicamos y comentamos aquí su testamento inédito, localizado en el Archivio di Stato di Roma entre los volúmenes del notario Thomassino, que se encargó del inventario de sus bienes, y aportamos noticias relativas a su herencia y a sus discípulos directos, Michele Alberti, Feliciano de San Vito y Biagio Betti, e indirectos, como Jacopo Rocchetti.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Quasi-integrability in the modified defocusing non-linear Schr\\"odinger model and dark solitons
Blas, H
2015-01-01
The concept of quasi-integrability has been examined in the context of deformations of the defocusing non-linear Schr\\"odinger model (NLS). Our results show that the quasi-integrability concept, recently discussed in the context of deformations of the sine-Gordon, Bullough-Dodd and focusing NLS models, holds for the modified defocusing NLS model with dark soliton solutions and it exhibits the new feature of an infinite sequence of alternating conserved and asymptotically conserved charges. For the special case of two dark soliton solutions, where the field components are eigenstates of a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved in the scattering process of the solitons. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. We perform extensive numerical simulations and consider the scattering of dark solitons for the cubic-quintic NLS model with potentia...
Existence of solutions for nonlinear mixed type integrodifferential equation of second order
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Haribhau Laxman Tidke
2010-04-01
Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.
Adaptive Kronrod-Patterson integration of non-linear finite-element matrices
DEFF Research Database (Denmark)
Janssen, Hans
2010-01-01
Efficient simulation of unsaturated moisture flow in porous media is of great importance in many engineering fields. The highly non-linear character of unsaturated flow typically gives sharp moving moisture fronts during wetting and drying of materials with strong local moisture permeability and ...
Proportional Plus Integral Control for Set-Point Regulation of a Class of Nonlinear RLC Circuits
Castanos, Fernando; Jayawardhana, Bayu; Ortega, Romeo; Garcia-Ganseco, Eloisa; García-Canseco, Eloísa
2009-01-01
In this paper we identify graph-theoretic conditions which allow us to write a nonlinear RLC circuit as port-Hamiltonian with constant input matrices. We show that under additional monotonicity conditions on the network's components, the circuit enjoys the property of relative passivity, an extended
Blom, F.C.; Driessen, A.; Hoekstra, Hugo; van Schoot, J.B.P.; van Schoot, Jan B.P.; Popma, T.J.A.
1999-01-01
In the long trajectory from the synthesis of organic nonlinear optical materials to the completed all-optical device it is highly desirable to be able to concentrate already in an early state on only a few promising materials. Third harmonic generation (THG) is a very convenient method as it allows
Blom, Freek C.; Driessen, Alfred; Hoekstra, Hugo J.W.M.; Schoot, van Jan B.P.; Popma, Th.J.A.
1999-01-01
In the long trajectory from the synthesis of organic nonlinear optical materials to the completed all-optical device it is highly desirable to be able to concentrate already in an early state on only a few promising materials. Third harmonic generation (THG) is a very convenient method as it allows
Directory of Open Access Journals (Sweden)
Sabir Djaidja
2014-01-01
Full Text Available Consensus of continuous-time single-integrator multiagent systems with inherent nonlinear dynamics and measurement noises is addressed in this paper. The consensus controller is developed for directed interaction topologies. Each agent’s control input is constructed based on its own state and its neighbors’ states corrupted by noises. The control input contains a time-varying consensus gain in order to attenuate the noises. Conditions for ensuring mean square convergence under noisy measurement and asymptotic convergence in the noise-free case are derived. Finally, some simulations were carried out to show the effectiveness of our control law and how it can solve the consensus problem.
Energy Technology Data Exchange (ETDEWEB)
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references.
Sinha, Debdeep; Ghosh, Pijush K.
2017-01-01
A two component nonlocal vector nonlinear Schrödinger equation (VNLSE) is considered with a self-induced parity-time-symmetric potential. It is shown that the system possess a Lax pair and an infinite number of conserved quantities and hence integrable. Some of the conserved quantities like number operator, Hamiltonian etc. are found to be real-valued, in spite of the corresponding charge densities being complex. The soliton solution for the same equation is obtained through the method of inverse scattering transformation and the condition of reduction from nonlocal to local case is mentioned.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Dual-point composition control for a high-purity ideal heat integrated distillation column (HIDiC) is addressed in this work. Three measures are suggested and combined for overcoming process inherent nonlinearities:(1) variable scaling; (2) multi-model representation of process dynamics and (3) feedforward compensation. These strategies can offer the developed control systems with several distinct advantages: (1) capability of dealing with severe disturbances; (2) tight tuning of controller parameters and (3) high robustness with respect to variation of operating conditions. Simulation results demonstrate the effectiveness of the proposed methodology.
Bruce, Kevin R.
1989-01-01
An integrated autopilot/autothrottle was designed for flight test on the NASA TSRV B-737 aircraft. The system was designed using a total energy concept and is attended to achieve the following: (1) fuel efficiency by minimizing throttle activity; (2) low development and implementation costs by designing the control modes around a fixed inner loop design; and (3) maximum safety by preventing stall and engine overboost. The control law was designed initially using linear analysis; the system was developed using nonlinear simulations. All primary design requirements were satisfied.
Lotka-Volterra systems in environments with randomly disordered temporal periodicity.
Naess, Arvid; Dimentberg, Michael F; Gaidai, Oleg
2008-08-01
A generalized Lotka-Volterra model for a pair of interacting populations of predators and prey is studied. The model accounts for the prey's interspecies competition and therefore is asymptotically stable, whereas its oscillatory behavior is induced by temporal variations in environmental conditions simulated by those in the prey's reproduction rate. Two models of the variations are considered, each of them combining randomness with "hidden" periodicity. The stationary joint probability density function (PDF) of the number of predators and prey is calculated numerically by the path integration (PI) method based on the use of characteristic functions and the fast Fourier transform. The numerical results match those for the asymptotic case of white-noise variations for which an analytical solution is available. Several examples are studied, with calculations of important characteristics of oscillations, for example the expected rate of up-crossings given the level of the predator number. The calculated PDFs may be of predominantly random (unimodal) or predominantly periodic nature (bimodal). Thus, the PI method has been demonstrated to be a powerful tool for studies of the dynamics of predator-prey pairs. The method captures the random oscillations as observed in nature, taking into account potential periodicity in the environmental conditions.
Fan, Quan-Yong; Yang, Guang-Hong
2016-01-01
This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.
Ilyas, Muhammad; Hong, Beomjin; Cho, Kuk; Baeg, Seung-Ho; Park, Sangdeok
2016-05-23
This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS) navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s) and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level.
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Muhammad Ilyas
2016-05-01
Full Text Available This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF and Unscented Kalman filter (UKF were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level.
Ilyas, Muhammad; Hong, Beomjin; Cho, Kuk; Baeg, Seung-Ho; Park, Sangdeok
2016-01-01
This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS) navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s) and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level. PMID:27223293
Directory of Open Access Journals (Sweden)
Hung-Chi Hsiao
2012-04-01
Full Text Available With the increasing cost of setting up a semiconductor fabrication facility, coupled with significant costs of developing a leading nanotechnology process, aggressive outsourcing (asset-light business models via working more closely with foundry companies is how semiconductor manufacturing firms are looking to strengthen their sustainable competitive advantages. This study aims to construct a market intelligence framework for developing a wafer demand forecasting model based on long-term trend detection to facilitate decision makers in capacity planning. The proposed framework modifies market variables by employing inventory factors and uses a top-down forecasting approach with nonlinear least square method to estimate the forecast parameters. The nonlinear mathematical approaches could not only be used to examine forecasting performance, but also to anticipate future growth of the semiconductor industry. The results demonstrated the practical viability of this long-term demand forecast framework.
Single-Photon Nonlinear Optics in Integrated Hollow-Core Waveguides
2010-10-13
for achieving the effective EIT as well as other nonlinear optics phenomena that rely on large optical depth. Here, we introduced a technique to...there is an interesting threshold phenomena with the increase of 194 195 signal power and after this threshold, the efficiency of idler generation...34, Optics Letters, 21, 1936-38, (1996). 27. V. Bali , D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of Paired Photons with
Institute of Scientific and Technical Information of China (English)
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
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Madden, Jeremy T.; Toth, Scott J.; Dettmar, Christopher M.; Newman, Justin A.; Oglesbee, Robert A.; Hedderich, Hartmut G.; Everly, R. Michael [Purdue University, 560 Oval Drive, West Lafayette, IN 47906 (United States); Becker, Michael [Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439 (United States); Ronau, Judith A. [Purdue University, 560 Oval Drive, West Lafayette, IN 47906 (United States); Buchanan, Susan K. [National Institutes of Health, Building 50, Room 4503, 50 South Drive, Bethesda, MD 20814 (United States); Cherezov, Vadim [The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, CA 92037 (United States); Morrow, Marie E. [Purdue University, 560 Oval Drive, West Lafayette, IN 47906 (United States); Xu, Shenglan; Ferguson, Dale; Makarov, Oleg [Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439 (United States); Das, Chittaranjan [Purdue University, 560 Oval Drive, West Lafayette, IN 47906 (United States); Fischetti, Robert [Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439 (United States); Simpson, Garth J., E-mail: gsimpson@purdue.edu [Purdue University, 560 Oval Drive, West Lafayette, IN 47906 (United States)
2013-07-01
Nonlinear optical (NLO) instrumentation has been integrated with synchrotron X-ray diffraction for combined single-platform analysis, examining the viability of NLO microscopy as an alternative to the conventional X-ray raster scan for the purposes of sample centering. Second-harmonic generation microscopy and two-photon excited ultraviolet fluorescence microscopy were evaluated for crystal detection, and assessed by X-ray raster scanning. Nonlinear optical (NLO) instrumentation has been integrated with synchrotron X-ray diffraction (XRD) for combined single-platform analysis, initially targeting applications for automated crystal centering. Second-harmonic-generation microscopy and two-photon-excited ultraviolet fluorescence microscopy were evaluated for crystal detection and assessed by X-ray raster scanning. Two optical designs were constructed and characterized; one positioned downstream of the sample and one integrated into the upstream optical path of the diffractometer. Both instruments enabled protein crystal identification with integration times between 80 and 150 µs per pixel, representing a ∼10{sup 3}–10{sup 4}-fold reduction in the per-pixel exposure time relative to X-ray raster scanning. Quantitative centering and analysis of phenylalanine hydroxylase from Chromobacterium violaceum cPAH, Trichinella spiralis deubiquitinating enzyme TsUCH37, human κ-opioid receptor complex kOR-T4L produced in lipidic cubic phase (LCP), intimin prepared in LCP, and α-cellulose samples were performed by collecting multiple NLO images. The crystalline samples were characterized by single-crystal diffraction patterns, while α-cellulose was characterized by fiber diffraction. Good agreement was observed between the sample positions identified by NLO and XRD raster measurements for all samples studied.
A time integral formulation and algorithm for structural dynamics with nonlinear stiffness
Institute of Scientific and Technical Information of China (English)
Kaiping Yu; Jie Zhao
2006-01-01
A newly-developed numerical algorithm, which is called the new Generalized-α(G-α)method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zerostable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.
Data-driven modeling based on volterra series for multidimensional blast furnace system.
Gao, Chuanhou; Jian, Ling; Liu, Xueyi; Chen, Jiming; Sun, Youxian
2011-12-01
The multidimensional blast furnace system is one of the most complex industrial systems and, as such, there are still many unsolved theoretical and experimental difficulties, such as silicon prediction and blast furnace automation. For this reason, this paper is concerned with developing data-driven models based on the Volterra series for this complex system. Three kinds of different low-order Volterra filters are designed to predict the hot metal silicon content collected from a pint-sized blast furnace, in which a sliding window technique is used to update the filter kernels timely. The predictive results indicate that the linear Volterra predictor can describe the evolvement of the studied silicon sequence effectively with the high percentage of hitting the target, very low root mean square error and satisfactory confidence level about the reliability of the future prediction. These advantages and the low computational complexity reveal that the sliding-window linear Volterra filter is full of potential for multidimensional blast furnace system. Also, the lack of the constructed Volterra models is analyzed and the possible direction of future investigation is pointed out.
Robinson, Brian S; Song, Dong; Berger, Theodore W
2013-01-01
This paper presents a Laguerre-Volterra methodology for identifying a plasticity learning rule from spiking neural data with four components: 1) By analyzing input-output spiking data, the effective contribution of an input on the output firing probability can be quantified with weighted Volterra kernels. 2) The weight of these Volterra kernels can be tracked over time using the stochastic state point processing filtering algorithm (SSPPF) 3) Plasticity system Volterra kernels can be estimated by treating the tracked change in weight over time as the plasticity system output and the spike timing data as the input. 4) Laguerre expansion of all Volterra kernels allows for minimization of open parameters during estimation steps. A single input spiking neuron with Spike-timing-dependent plasticity (STDP) and prolonged STDP induction is simulated. Using the spiking data from this simulation, the amplitude of the STDP learning rule and the time course of the induction is accurately estimated. This framework can be applied to identify plasticity for more complicated plasticity paradigms and is applicable to in vivo data.
Online Fault Diagnosis Method Based on Nonlinear Spectral Analysis
Institute of Scientific and Technical Information of China (English)
WEI Rui-xuan; WU Li-xun; WANG Yong-chang; HAN Chong-zhao
2005-01-01
The fault diagnosis based on nonlinear spectral analysis is a new technique for the nonlinear fault diagnosis, but its online application could be limited because of the enormous compution requirements for the estimation of general frequency response functions. Based on the fully decoupled Volterra identification algorithm, a new online fault diagnosis method based on nonlinear spectral analysis is presented, which can availably reduce the online compution requirements of general frequency response functions. The composition and working principle of the method are described, the test experiments have been done for damping spring of a vehicle suspension system by utilizing the new method, and the results indicate that the method is efficient.
Directory of Open Access Journals (Sweden)
Yange Huang
2014-01-01
Full Text Available We discuss a class of Volterra-Fredholm type difference inequalities with weakly singular. The upper bounds of the embedded unknown functions are estimated explicitly by analysis techniques. An application of the obtained inequalities to the estimation of Volterra-Fredholm type difference equations is given.
HOC Based Blind Identification of Hydroturbine Shaft Volterra System
Directory of Open Access Journals (Sweden)
Bing Bai
2017-01-01
Full Text Available In order to identify the quadratic Volterra system simplified from the hydroturbine shaft system, a blind identification method based on the third-order cumulants and a reversely recursive method are proposed. The input sequence of the system under consideration is an unobservable independent identically distributed (i.i.d., zero-mean and non-Gaussian stationary signal, and the observed signals are the superposition of the system output signal and Gaussian noise. To calculate the third-order moment of the output signal, a computer loop judgment method is put forward to determine the coefficient. When using optimization method to identify the time domain kernels, we combined the traditional optimization algorithm (direct search method with genetic algorithm (GA and constituted the hybrid genetic algorithm (HGA. Finally, according to the prototype observation signal and the time domain kernel parameters obtained from identification, the input signal of the system can be gained recursively. To test the proposed method, three numerical experiments and engineering application have been carried out. The results show that the method is applicable to the blind identification of the hydroturbine shaft system and has strong universality; the input signal obtained by the reversely recursive method can be approximately taken as the random excitation acted on the runner of the hydroturbine shaft system.
Lotka-Volterra system in a random environment
Dimentberg, Mikhail F.
2002-03-01
Classical Lotka-Volterra (LV) model for oscillatory behavior of population sizes of two interacting species (predator-prey or parasite-host pairs) is conservative. This may imply unrealistically high sensitivity of the system's behavior to environmental variations. Thus, a generalized LV model is considered with the equation for preys' reproduction containing the following additional terms: quadratic ``damping'' term that accounts for interspecies competition, and term with white-noise random variations of the preys' reproduction factor that simulates the environmental variations. An exact solution is obtained for the corresponding Fokker-Planck-Kolmogorov equation for stationary probability densities (PDF's) of the population sizes. It shows that both population sizes are independent γ-distributed stationary random processes. Increasing level of the environmental variations does not lead to extinction of the populations. However it may lead to an intermittent behavior, whereby one or both population sizes experience very rare and violent short pulses or outbreaks while remaining on a very low level most of the time. This intermittency is described analytically by direct use of the solutions for the PDF's as well as by applying theory of excursions of random functions and by predicting PDF of peaks in the predators' population size.
Food Web Assembly Rules for Generalized Lotka-Volterra Equations.
Directory of Open Access Journals (Sweden)
Jan O Haerter
2016-02-01
Full Text Available In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.
Lotka-Volterra system in a random environment.
Dimentberg, Mikhail F
2002-03-01
Classical Lotka-Volterra (LV) model for oscillatory behavior of population sizes of two interacting species (predator-prey or parasite-host pairs) is conservative. This may imply unrealistically high sensitivity of the system's behavior to environmental variations. Thus, a generalized LV model is considered with the equation for preys' reproduction containing the following additional terms: quadratic "damping" term that accounts for interspecies competition, and term with white-noise random variations of the preys' reproduction factor that simulates the environmental variations. An exact solution is obtained for the corresponding Fokker-Planck-Kolmogorov equation for stationary probability densities (PDF's) of the population sizes. It shows that both population sizes are independent gamma-distributed stationary random processes. Increasing level of the environmental variations does not lead to extinction of the populations. However it may lead to an intermittent behavior, whereby one or both population sizes experience very rare and violent short pulses or outbreaks while remaining on a very low level most of the time. This intermittency is described analytically by direct use of the solutions for the PDF's as well as by applying theory of excursions of random functions and by predicting PDF of peaks in the predators' population size.
Fractal properties of the lattice Lotka-Volterra model.
Tsekouras, G A; Provata, A
2002-01-01
The lattice Lotka-Volterra (LLV) model is studied using mean-field analysis and Monte Carlo simulations. While the mean-field phase portrait consists of a center surrounded by an infinity of closed trajectories, when the process is restricted to a two-dimensional (2D) square lattice, local inhomogeneities/fluctuations appear. Spontaneous local clustering is observed on lattice and homogeneous initial distributions turn into clustered structures. Reactions take place only at the interfaces between different species and the borders adopt locally fractal structure. Intercluster surface reactions are responsible for the formation of local fluctuations of the species concentrations. The box-counting fractal dimension of the LLV dynamics on a 2D support is found to depend on the reaction constants while the upper bound of fractality determines the size of the local oscillators. Lacunarity analysis is used to determine the degree of clustering of homologous species. Besides the spontaneous clustering that takes place on a regular 2D lattice, the effects of fractal supports on the dynamics of the LLV are studied. For supports of dimensionality D(s)<2 the lattice can, for certain domains of the reaction constants, adopt a poisoned state where only one of the species survives. By appropriately selecting the fractal dimension of the substrate, it is possible to direct the system into a poisoned or oscillatory steady state at will.
Food Web Assembly Rules for Generalized Lotka-Volterra Equations.
Haerter, Jan O; Mitarai, Namiko; Sneppen, Kim
2016-02-01
In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.
Khachatryan, Kh A.
2015-04-01
We study certain classes of non-linear Hammerstein integral equations on the semi-axis and the whole line. These classes of equations arise in the theory of radiative transfer in nuclear reactors, in the kinetic theory of gases, and for travelling waves in non-linear Richer competition systems. By combining special iteration methods with the methods of construction of invariant cone segments for the appropriate non-linear operator, we are able to prove constructive existence theorems for positive solutions in various function spaces. We give illustrative examples of equations satisfying all the hypotheses of our theorems.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
Gerbeau, Jean-Frédéric; Lombardi, Damiano
2014-05-01
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive front or wave propagation. Another difference with other reduced-order methods is that it is not based on an off-line/on-line strategy. Numerical examples are shown for the linear advection, KdV and FKPP equations, in one and two dimensions.
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
The Jungle Universe: coupled cosmological models in a Lotka-Volterra framework
Perez, Jérôme; Füzfa, André; Carletti, Timoteo; Mélot, Laurence; Guedezounme, Lazare
2014-06-01
In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaître universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaître cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserves the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.
Krishnan, Venkatarama
2005-01-01
Most useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value.After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping time
Altürk, Ahmet
2016-01-01
Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some ...
On the connection between hyperelliptic separability and Painleve integrability
Energy Technology Data Exchange (ETDEWEB)
Abenda, S. [Dipartimento di Matematica e CIRAM, Universita' di Bologna, Bologna BO (Italy); Marinakis, V.; Bountis, T. [Department of Mathematics and Centre for Research and Application of Nonlinear Systems, University of Patras, Patras (Greece)
2001-05-04
We consider systems of ODEs which are associated with some physically significant examples: shallow water equilibrium solutions, travelling waves of the Harry Dym equation, a Lotka-Volterra system of competing species and the geodesic flow on the triaxial ellipsoid. The first three are shown to share the following properties: (i) they are hyperelliptically separable systems (HSS) and, after a suitable nonlinear time transformation, become algebraically completely integrable (ACI) and (ii) they are of the weak Painleve type and become full Painleve after the application of this transformation. The geodesic flow on the other hand, although it passes the usual Painleve test, does not possess a full set of free constants and thus one may not conclude whether it has the Painleve property or not. This system is also HSS and becomes ACI after the application of a suitable nonlinear time transformation. We also combine our geometric-analytical investigation with a numerical analysis of the system in the complex plane and show that there is perfect correspondence between the results of the two approaches. This correspondence strengthens the reliability of such numerical studies and helps us better understand their implication in cases where such nonlinear transformations to complete integrability are not available. (author)
Ning, Hanwen; Qing, Guangyan; Jing, Xingjian
2016-11-01
The identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades. Several methods, such as searching principle-based algorithms, partially linear kernel methods, and coupled lattice methods, have been developed to address the identification problems. However, most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains. These are actually not applicable for some practical applications. In this paper, to tackle this issue, a novel kernel-based learning algorithm named integral least square regularization regression (ILSRR) is proposed, which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain. With this technique, a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified. Thereafter, with this novel inverse meshless collocation model, the ILSRR, and a multiple-kernel-based learning algorithm, a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations. Numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method.
Kaabi, Mohamed Ghaith; Tonnelier, Arnaud; Martinez, Dominique
2011-05-01
In traditional event-driven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrate-and-fire model. In a recent paper, Zheng, Tonnelier, and Martinez (2009) introduced an approximate event-driven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrate-and-fire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrate-and-fire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified time-stepping scheme of the Runge-Kutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity.
Institute of Scientific and Technical Information of China (English)
滕志东
2001-01-01
In this paper, the permanence and extinction of general nonautonomous N-species Lotka-Volterra type competitive systems with pure-delays are studied. Some new criteria are established. The results obtained in [8-10] for nondelayed nonau-tonomous Lotka-Volterra type competitive systems are improved and extended.%本文研究具有纯时滞的一般N-种群非自治Lotka-Volterra竞争系统的持久性和灭绝性.一些新的判别准则被建立.文献[8-10]中得到的关于无时滞非自治Lotka-Volterra竞争系统的结果被改进和推广.
Energy Technology Data Exchange (ETDEWEB)
Skokos, Ch., E-mail: haris.skokos@uct.ac.za [Physics Department, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701 (South Africa); Gerlach, E. [Lohrmann Observatory, Technical University Dresden, D-01062 Dresden (Germany); Bodyfelt, J.D., E-mail: J.Bodyfelt@massey.ac.nz [Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Albany, Private Bag 102904, North Shore City, Auckland 0745 (New Zealand); Papamikos, G. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Eggl, S. [IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014 Paris (France)
2014-05-01
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we present several high order symplectic integrators for Hamiltonian systems that can be split in exactly three integrable parts. We apply these techniques, as a practical case, for the integration of the disordered, discrete nonlinear Schrödinger equation (DDNLS) and compare their efficiencies. Three part split algorithms provide effective means to numerically study the asymptotic behavior of wave packet spreading in the DDNLS – a hotly debated subject in current scientific literature.
Bds/gps Integrated Positioning Method Research Based on Nonlinear Kalman Filtering
Ma, Y.; Yuan, W.; Sun, H.
2017-09-01
In order to realize fast and accurate BDS/GPS integrated positioning, it is necessary to overcome the adverse effects of signal attenuation, multipath effect and echo interference to ensure the result of continuous and accurate navigation and positioning. In this paper, pseudo-range positioning is used as the mathematical model. In the stage of data preprocessing, using precise and smooth carrier phase measurement value to promote the rough pseudo-range measurement value without ambiguity. At last, the Extended Kalman Filter(EKF), the Unscented Kalman Filter(UKF) and the Particle Filter(PF) algorithm are applied in the integrated positioning method for higher positioning accuracy. The experimental results show that the positioning accuracy of PF is the highest, and UKF is better than EKF.
Huang, C Q; Xie, L F; Liu, Y L
2012-11-01
In framework of traditional PID controllers, there are only three parameters available to tune, as a result, performance of the resulting system is always limited. As for Cartesian regulation of robot manipulators with uncertain Jacobian matrix, a scheme of PID controllers with error-dependent integral action is proposed. Compare with traditional PID controllers, the error-dependent integration is employed in the proposed PID controller, in which more parameters are available to be tuned. It provides additional flexibility for controller characteristics and tuning as well, and hence makes better transient performance. In addition, asymptotic stability of the resulting closed-loop system is guaranteed. All signals in the system are bounded when exogenous disturbances and measurement noises are bounded. Numerical example demonstrates the superior transient performance of the proposed controller over the traditional one via Cartesian space set-point manipulation of two-link robotic manipulator.