WorldWideScience

Sample records for nonlinear evolution systems

  1. Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Kostov, N.A.

    1989-01-01

    In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs

  2. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  3. Solving nonlinear evolution equation system using two different methods

    Science.gov (United States)

    Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.

    2015-12-01

    This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

  4. Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

    International Nuclear Information System (INIS)

    Maccari, A.

    1997-01-01

    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 universalclose quotes character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. copyright 1997 American Institute of Physics

  5. Nonlinear evolution of MHD instabilities

    International Nuclear Information System (INIS)

    Bateman, G.; Hicks, H.R.; Wooten, J.W.; Dory, R.A.

    1975-01-01

    A 3-D nonlinear MHD computer code was used to study the time evolution of internal instabilities. Velocity vortex cells are observed to persist into the nonlinear evolution. Pressure and density profiles convect around these cells for a weak localized instability, or convect into the wall for a strong instability. (U.S.)

  6. Nonlinear systems

    CERN Document Server

    Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús

    2018-01-01

    This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

  7. Identification of time-varying nonlinear systems using differential evolution algorithm

    DEFF Research Database (Denmark)

    Perisic, Nevena; Green, Peter L; Worden, Keith

    2013-01-01

    (DE) algorithm for the identification of time-varying systems. DE is an evolutionary optimisation method developed to perform direct search in a continuous space without requiring any derivative estimation. DE is modified so that the objective function changes with time to account for the continuing......, thus identification of time-varying systems with nonlinearities can be a very challenging task. In order to avoid conventional least squares and gradient identification methods which require uni-modal and double differentiable objective functions, this work proposes a modified differential evolution...... inclusion of new data within an error metric. This paper presents results of identification of a time-varying SDOF system with Coulomb friction using simulated noise-free and noisy data for the case of time-varying friction coefficient, stiffness and damping. The obtained results are promising and the focus...

  8. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  9. Evolution Of Nonlinear Waves in Compressing Plasma

    International Nuclear Information System (INIS)

    Schmit, P.F.; Dodin, I.Y.; Fisch, N.J.

    2011-01-01

    Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size Δ during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches Δ. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.

  10. Evolution Of Nonlinear Waves in Compressing Plasma

    Energy Technology Data Exchange (ETDEWEB)

    P.F. Schmit, I.Y. Dodin, and N.J. Fisch

    2011-05-27

    Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.

  11. Nonlinear systems

    National Research Council Canada - National Science Library

    Drazin, P. G

    1992-01-01

    This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...

  12. Simulating nonlinear neutrino flavor evolution

    Science.gov (United States)

    Duan, H.; Fuller, G. M.; Carlson, J.

    2008-10-01

    We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev Smirnov Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle θ13.

  13. Decomposition of a hierarchy of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Geng Xianguo

    2003-01-01

    The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations

  14. Improved Minimum Entropy Filtering for Continuous Nonlinear Non-Gaussian Systems Using a Generalized Density Evolution Equation

    Directory of Open Access Journals (Sweden)

    Jinliang Xu

    2013-06-01

    Full Text Available This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF.

  15. Simulating nonlinear neutrino flavor evolution

    Energy Technology Data Exchange (ETDEWEB)

    Duan, H [Institute for Nuclear Theory, University of Washington, Seattle, WA 98195 (United States); Fuller, G M [Department of Physics, University of California, San Diego, La Jolla, CA 92093 (United States); Carlson, J [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)], E-mail: hduan@phys.washington.edu, E-mail: gfuller@ucsd.edu, E-mail: carlson@lanl.gov

    2008-10-01

    We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev-Smirnov-Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle {theta}{sub 13}.

  16. Nonlinear Evolution of Alfvenic Wave Packets

    Science.gov (United States)

    Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.

    1998-01-01

    Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.

  17. Saturation at Low X and Nonlinear Evolution

    International Nuclear Information System (INIS)

    Stasto, A.M.

    2002-01-01

    In this talk the results of the analytical and numerical analysis of the nonlinear Balitsky-Kovchegov equation are presented. The characteristic BFKL diffusion into infrared regime is suppressed by the generation of the saturation scale Q s . We identify the scaling and linear regimes for the solution. We also study the impact of subleading corrections onto the nonlinear evolution. (author)

  18. First Integrals of Evolution Systems and Nonlinear Stability of Stationary Solutions for the Ideal Atmospheric, Oceanic Hydrodynamical and Plasma Models

    International Nuclear Information System (INIS)

    Gordin, V.A.

    1998-01-01

    First integral of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. (author)

  19. Energy dependence of the Cronin effect from nonlinear QCD evolution

    International Nuclear Information System (INIS)

    Albacete, Javier L.; Armesto, Nestor; Salgado, Carlos A.; Wiedemann, Urs Achim; Kovner, Alex

    2004-01-01

    The nonlinear evolution of dense partonic systems has been suggested as a novel physics mechanism relevant for the dynamics of p-A and A-A collisions at collider energies. Here we study to what extent the description of Cronin enhancement in the framework of this nonlinear evolution is consistent with the recent observation in √(s)=200 GeV d-Au collisions at the Relativistic Heavy Ion Collider. We solve the Balitsky-Kovchegov evolution equation numerically for several initial conditions encoding Cronin enhancement. We find that the properly normalized nuclear gluon distribution is suppressed at all momenta relative to that of a single nucleon. For the resulting spectrum of produced gluons in p-A and A-A collisions, the nonlinear QCD evolution is unable to generate a Cronin-type enhancement, and it quickly erases any such enhancement which may be present at lower energies

  20. Nonlinear optical systems

    CERN Document Server

    Lugiato, Luigi; Brambilla, Massimo

    2015-01-01

    Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

  1. Correlations and discreteness in nonlinear QCD evolution

    International Nuclear Information System (INIS)

    Armesto, N.; Milhano, J.

    2006-01-01

    We consider modifications of the standard nonlinear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities y=(α s N c /π)Y<10. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cutoff evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cutoff. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients

  2. Nonlinear evolution of astrophysical Alfven waves

    Science.gov (United States)

    Spangler, S. R.

    1984-01-01

    Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.

  3. Balancing for nonlinear systems

    NARCIS (Netherlands)

    Scherpen, J.M.A.

    1993-01-01

    We present a method of balancing for nonlinear systems which is an extension of balancing for linear systems in the sense that it is based on the input and output energy of a system. It is a local result, but gives 'broader' results than we obtain by just linearizing the system. Furthermore, the

  4. Nonlinear evolution equations having a physical meaning

    International Nuclear Information System (INIS)

    Nakach, R.

    1976-06-01

    The non stationary self-similar solutions of the nonlinear evolution equations which can be solved by the inverse scattering method are studied. It turns out, as shown by means of several examples, that when the L linear operator associated with these equations, is of second order and only then, the self-similar solutions can be expressed in terms of the various Painleve's transcendents [fr

  5. Oscillations in nonlinear systems

    CERN Document Server

    Hale, Jack K

    2015-01-01

    By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

  6. Fluctuations in Nonlinear Systems: A Short Review

    International Nuclear Information System (INIS)

    Rubia, F.J. de la; Buceta, J.; Cabrera, J.L.; Olarrea, J.; Parrondo, J.M.R.

    2003-01-01

    We review some results that illustrate the constructive role of noise in nonlinear systems. Several phenomena are briefly discussed: optimal localization of orbits in a system with limit cycle behavior and perturbed by colored noise; stochastic branch selection at secondary bifurcations; noise- induced order/disorder transitions and pattern formation in spatially extended systems. In all cases the presence of noise is crucial, and the results reinforce the modern view of the importance of noise in the evolution of nonlinear systems. (author)

  7. 3-D nonlinear evolution of MHD instabilities

    International Nuclear Information System (INIS)

    Bateman, G.; Hicks, H.R.; Wooten, J.W.

    1977-03-01

    The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed

  8. Nonlinear Hamiltonian systems

    DEFF Research Database (Denmark)

    Jørgensen, Michael Finn

    1995-01-01

    It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

  9. Space and time evolution of two nonlinearly coupled variables

    International Nuclear Information System (INIS)

    Obayashi, H.; Totsuji, H.; Wilhelmsson, H.

    1976-12-01

    The system of two coupled linear differential equations are studied assuming that the coupling terms are proportional to the product of the dependent variables, representing e.g. intensities or populations. It is furthermore assumed that these variables experience different linear dissipation or growth. The derivations account for space as well as time dependence of the variables. It is found that certain particular solutions can be obtained to this system, whereas a full solution in space and time as an initial value problem is outside the scope of the present paper. The system has a nonlinear equilibrium solution for which the nonlinear coupling terms balance the terms of linear dissipation. The case of space and time evolution of a small perturbation of the nonlinear equilibrium state, given the initial one-dimensional spatial distribution of the perturbation, is also considered in some detail. (auth.)

  10. H∞ Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, Jacquelien M.A.

    1996-01-01

    In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define

  11. A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems

    International Nuclear Information System (INIS)

    Banerjee, Amit; Abu-Mahfouz, Issam

    2014-01-01

    The use of evolutionary algorithms has been popular in recent years for solving the inverse problem of identifying system parameters given the chaotic response of a dynamical system. The inverse problem is reformulated as a minimization problem and population-based optimizers such as evolutionary algorithms have been shown to be efficient solvers of the minimization problem. However, to the best of our knowledge, there has been no published work that evaluates the efficacy of using the two most popular evolutionary techniques – particle swarm optimization and differential evolution algorithm, on a wide range of parameter estimation problems. In this paper, the two methods along with their variants (for a total of seven algorithms) are applied to fifteen different parameter estimation problems of varying degrees of complexity. Estimation results are analyzed using nonparametric statistical methods to identify if an algorithm is statistically superior to others over the class of problems analyzed. Results based on parameter estimation quality suggest that there are significant differences between the algorithms with the newer, more sophisticated algorithms performing better than their canonical versions. More importantly, significant differences were also found among variants of the particle swarm optimizer and the best performing differential evolution algorithm

  12. FRF decoupling of nonlinear systems

    Science.gov (United States)

    Kalaycıoğlu, Taner; Özgüven, H. Nevzat

    2018-03-01

    Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

  13. Balancing for Unstable Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, J.M.A.

    1993-01-01

    A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By

  14. Spectral transform and solvability of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Degasperis, A.

    1979-01-01

    These lectures deal with an exciting development of the last decade, namely the resolving method based on the spectral transform which can be considered as an extension of the Fourier analysis to nonlinear evolution equations. Since many important physical phenomena are modeled by nonlinear partial wave equations this method is certainly a major breakthrough in mathematical physics. We follow the approach, introduced by Calogero, which generalizes the usual Wronskian relations for solutions of a Sturm-Liouville problem. Its application to the multichannel Schroedinger problem will be the subject of these lectures. We will focus upon dynamical systems described at time t by a multicomponent field depending on one space coordinate only. After recalling the Fourier technique for linear evolution equations we introduce the spectral transform method taking the integral equations of potential scattering as an example. The second part contains all the basic functional relationships between the fields and their spectral transforms as derived from the Wronskian approach. In the third part we discuss a particular class of solutions of nonlinear evolution equations, solitons, which are considered by many physicists as a first step towards an elementary particle theory, because of their particle-like behaviour. The effect of the polarization time-dependence on the motion of the soliton is studied by means of the corresponding spectral transform, leading to new concepts such as the 'boomeron' and the 'trappon'. The rich dynamic structure is illustrated by a brief report on the main results of boomeron-boomeron and boomeron-trappon collisions. In the final section we discuss further results concerning important properties of the solutions of basic nonlinear equations. We introduce the Baecklund transform for the special case of scalar fields and demonstrate how it can be used to generate multisoliton solutions and how the conservation laws are obtained. (HJ)

  15. Nonlinear evolutions of bosonic clouds around black holes

    International Nuclear Information System (INIS)

    Okawa, Hirotada

    2015-01-01

    Black holes are a laboratory not only for testing the theory of gravity but also for exploring the properties of fundamental fields. Fundamental fields around a supermassive black hole give rise to extremely long-lived quasi-bound states which can in principle extract the energy and angular momentum from the black hole. To investigate the final state of such a system, the backreaction onto the spacetime becomes important because of the nonlinearity of the Einstein equation. In this paper, we review the numerical method to trace the evolution of massive scalar fields in the vicinity of black holes, how such a system originates from scalar clouds initially in the absence of black holes or from the capture of scalar clouds by a black hole, and the evolution of quasi-bound states around both a non-rotating black hole and a rotating black hole including the backreaction. (paper)

  16. On a new series of integrable nonlinear evolution equations

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.

    1980-10-01

    Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)

  17. Analytic treatment of nonlinear evolution equations using first ...

    Indian Academy of Sciences (India)

    1. — journal of. July 2012 physics pp. 3–17. Analytic treatment of nonlinear evolution ... Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics, ... (2.2) is integrated where integration constants are considered zeros.

  18. Approximate viability for nonlinear evolution inclusions with application to controllability

    Directory of Open Access Journals (Sweden)

    Omar Benniche

    2016-12-01

    Full Text Available We investigate approximate viability for a graph with respect to fully nonlinear quasi-autonomous evolution inclusions. As application, an approximate null controllability result is given.

  19. Hamiltonian structures of some non-linear evolution equations

    International Nuclear Information System (INIS)

    Tu, G.Z.

    1983-06-01

    The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

  20. Topological soliton solutions for some nonlinear evolution equations

    Directory of Open Access Journals (Sweden)

    Ahmet Bekir

    2014-03-01

    Full Text Available In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc. envelope for the understanding of most nonlinear physical phenomena.

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

    Indian Academy of Sciences (India)

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

  2. New travelling wave solutions for nonlinear stochastic evolution

    Indian Academy of Sciences (India)

    The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...

  3. Prolongation Structure of Semi-discrete Nonlinear Evolution Equations

    International Nuclear Information System (INIS)

    Bai Yongqiang; Wu Ke; Zhao Weizhong; Guo Hanying

    2007-01-01

    Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schroedinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.

  4. Long wavelength limit of evolution of nonlinear cosmological perturbations

    International Nuclear Information System (INIS)

    Hamazaki, Takashi

    2008-01-01

    In the general matter composition where the multiple scalar fields and the multiple perfect fluids coexist, in the leading order of the gradient expansion, we construct all of the solutions of the nonlinear evolutions of the locally homogeneous universe. From the momentum constraint, we derive the constraints which the solution constants of the locally homogeneous universe must satisfy. We construct the gauge invariant perturbation variables in the arbitrarily higher order nonlinear cosmological perturbation theory around the spatially flat Friedmann-Robertson-Walker universe. We construct the nonlinear long wavelength limit formula representing the long wavelength limit of the evolution of the nonlinear gauge invariant perturbation variables in terms of perturbations of the evolutions of the locally homogeneous universe. By using the long wavelength limit formula, we investigate the evolution of nonlinear cosmological perturbations in the universe dominated by the multiple slow rolling scalar fields with an arbitrary potential. The τ function and the N potential introduced in this paper make it possible to write the evolution of the multiple slow rolling scalar fields with an arbitrary interaction potential and the arbitrarily higher order nonlinear Bardeen parameter at the end of the slow rolling phase analytically. It is shown that the nonlinear parameters such as f NL and g NL are suppressed by the slow rolling expansion parameters.

  5. Initial evolution of nonlinear magnetic islands in high temperature plasmas

    International Nuclear Information System (INIS)

    Kotschenreuther, M.

    1988-06-01

    The evolution of nonlinear magnetic islands is computed in the kinetic collisionality regime called the semicollisional regime, which is appropriate to present fusion confinement devices. Realistic effects are included, such as the presence of small external field errors, radial electric fields, and omega. When present simultaneously, these effects can greatly change the stability of small amplitude nonlinear islands. Islands with Δ' > O can sometimes be prevented from growing to macroscopic size; it is also possible to produce moderate mode-number nonlinear instabilities in the plasma edge. Furthermore, island growth can be prevented by application of external fields with suitably chosen amplitude and frequency

  6. Nonlinear evolution equations for waves in random media

    International Nuclear Information System (INIS)

    Pelinovsky, E.; Talipova, T.

    1994-01-01

    The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs

  7. Shear flows induced by nonlinear evolution of double tearing modes

    International Nuclear Information System (INIS)

    Wang Zhengxiong; Kishimoto, Y.; Li, J. Q.; Wang Xiaogang; Dong, J. Q.

    2008-01-01

    Shear flows induced by nonlinear evolution of double tearing modes are investigated in a resistive magnetohydrodynamic model with slab geometry. It is found that intensive and thin poloidal shear flow layers are generated in the magnetic island region driven by coupled reconnection process at both rational surfaces. The structure of the flow layers keeps evolving after the merging of magnetic separatrices and forms a few narrow vortices along the open field lines in the final stage of magnetic reconnection. The effects of the distance between both rational surfaces and the initial magnetic shear on the nonlinear evolution of the plasma flows are also taken into consideration and the relevant mechanism is discussed

  8. Nonlinear robust hierarchical control for nonlinear uncertain systems

    Directory of Open Access Journals (Sweden)

    Leonessa Alexander

    1999-01-01

    Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

  9. Nonlinear transport of dynamic system phase space

    International Nuclear Information System (INIS)

    Xie Xi; Xia Jiawen

    1993-01-01

    The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

  10. NONLINEAR EVOLUTION OF GLOBAL HYDRODYNAMIC SHALLOW-WATER INSTABILITY IN THE SOLAR TACHOCLINE

    International Nuclear Information System (INIS)

    Dikpati, Mausumi

    2012-01-01

    We present a fully nonlinear hydrodynamic 'shallow-water' model of the solar tachocline. The model consists of a global spherical shell of differentially rotating fluid, which has a deformable top, thus allowing motions in radial directions along with latitudinal and longitudinal directions. When the system is perturbed, in the course of its nonlinear evolution it can generate unstable low-frequency shallow-water shear modes from the differential rotation, high-frequency gravity waves, and their interactions. Radiative and overshoot tachoclines are characterized in this model by high and low effective gravity values, respectively. Building a semi-implicit spectral scheme containing very low numerical diffusion, we perform nonlinear evolution of shallow-water modes. Our first results show that (1) high-latitude jets or polar spin-up occurs due to nonlinear evolution of unstable hydrodynamic shallow-water disturbances and differential rotation, (2) Reynolds stresses in the disturbances together with changing shell thickness and meridional flow are responsible for the evolution of differential rotation, (3) disturbance energy primarily remains concentrated in the lowest longitudinal wavenumbers, (4) an oscillation in energy between perturbed and unperturbed states occurs due to evolution of these modes in a nearly dissipation-free system, and (5) disturbances are geostrophic, but occasional nonadjustment in geostrophic balance can occur, particularly in the case of high effective gravity, leading to generation of gravity waves. We also find that a linearly stable differential rotation profile remains nonlinearly stable.

  11. Nonlinear second order evolution inclusions with noncoercive viscosity term

    Science.gov (United States)

    Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.

    2018-04-01

    In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.

  12. Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations

    International Nuclear Information System (INIS)

    Yu Jianping; Sun Yongli

    2008-01-01

    This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation. Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations

  13. Nonlinear evolution of the sausage instability

    International Nuclear Information System (INIS)

    Book, D.L.; Ott, E.; Lampe, M.

    1976-01-01

    Sausage instabilities of an incompressible, uniform, perfectly conducting Z pinch are studied in the nonlinear regime. In the long wavelength limit (analogous to the ''shallow water theory'' of hydrodynamics), a simplified set of universal fluid equations is derived, with no radial dependence, and with all parameters scaled out. Analytic and numerical solutions of these one-dimensional equations show that an initially sinusoidal perturbation grows into a ''spindle'' or cylindrical ''spike and bubble'' shape, with sharp radial maxima. In the short wavelength limit, the problem is shown to be mathematically equivalent to the planar semi-infinite Rayleigh--Taylor instability, which also grows into a spike-and-bubble shape. Since the spindle shape is common to both limits, it is concluded that it probably obtains in all cases. The results are in agreement with dense plasma focus experiments

  14. Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

    Directory of Open Access Journals (Sweden)

    Jun Wang

    2013-01-01

    Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

  15. Nonlinear dynamics in biological systems

    CERN Document Server

    Carballido-Landeira, Jorge

    2016-01-01

    This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...

  16. Spectral decomposition of nonlinear systems with memory

    Science.gov (United States)

    Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

    2016-02-01

    We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

  17. Frequency response functions for nonlinear convergent systems

    NARCIS (Netherlands)

    Pavlov, A.V.; Wouw, van de N.; Nijmeijer, H.

    2007-01-01

    Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency

  18. New generalized and improved (G′/G-expansion method for nonlinear evolution equations in mathematical physics

    Directory of Open Access Journals (Sweden)

    Hasibun Naher

    2014-10-01

    Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.

  19. NONLINEAR TIDES IN CLOSE BINARY SYSTEMS

    International Nuclear Information System (INIS)

    Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

    2012-01-01

    We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' ∼> 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P ∼ 3 [P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P ∼< a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing

  20. Nonlinear wave evolution in VLASOV plasma: a lie-transform analysis

    International Nuclear Information System (INIS)

    Cary, J.R.

    1979-08-01

    Nonlinear wave evolution in Vlasov plasma is analyzed using the Lie transform, a powerful mathematical tool which is applicable to Hamiltonian systems. The first part of this thesis is an exposition of the Lie transform. Dewar's general Lie transform theory is explained and is used to construct Deprit's Lie transform perturbation technique. The basic theory is illustrated by simple examples

  1. Loss of Energy Concentration in Nonlinear Evolution Beam Equations

    Science.gov (United States)

    Garrione, Maurizio; Gazzola, Filippo

    2017-12-01

    Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we introduce the notion of solutions with a prevailing mode for the nonlinear evolution beam equation u_{tt} + u_{xxxx} + f(u)= g(x, t) in bounded space-time intervals. We give a new definition of instability for these particular solutions, based on the loss of energy concentration on their prevailing mode. We distinguish between two different forms of energy transfer, one physiological (unavoidable and depending on the nonlinearity) and one due to the insurgence of instability. We then prove a theoretical result allowing to reduce the study of this kind of infinite-dimensional stability to that of a finite-dimensional approximation. With this background, we study the occurrence of instability for three different kinds of nonlinearities f and for some forcing terms g, highlighting some of their structural properties and performing some numerical simulations.

  2. Complex motions and chaos in nonlinear systems

    CERN Document Server

    Machado, José; Zhang, Jiazhong

    2016-01-01

    This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.

  3. Nonlinear evolution inclusions arising from phase change models

    Czech Academy of Sciences Publication Activity Database

    Colli, P.; Krejčí, Pavel; Rocca, E.; Sprekels, J.

    2007-01-01

    Roč. 57, č. 4 (2007), s. 1067-1098 ISSN 0011-4642 R&D Projects: GA ČR GA201/02/1058 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear and nonlocal evolution equations * Cahn-Hilliard type dynamics * phase transitions models Subject RIV: BA - General Mathematics Impact factor: 0.155, year: 2007 http://www.dml.cz/bitstream/handle/10338.dmlcz/128228/CzechMathJ_57-2007-4_2.pdf

  4. Nonlinear evolution of single spike in Richtmyer-Meshkov instability

    International Nuclear Information System (INIS)

    Fukuda, Y.; Nishihara, K.; Wouchuk, J.G.

    2000-01-01

    Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated with the use of a two-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. (authors)

  5. Nonlinear evolution of Mack modes in a hypersonic boundary layer

    Science.gov (United States)

    Chokani, Ndaona

    2005-01-01

    In hypersonic boundary layer flows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layer transition. In the case of low-level freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Cross-bicoherence measurements, derived from hot-wire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phase-locked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, cross-bicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the low-frequency, phase-locked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.

  6. Nonlinear time heteronymous damping in nonlinear parametric planetary systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena

    2014-01-01

    Roč. 225, č. 7 (2014), s. 2059-2073 ISSN 0001-5970 Institutional support: RVO:61388998 Keywords : nonlinear dynamics * planetary systems * heteronymous damping Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 1.465, year: 2014

  7. Nonlinearity of colloid systems oxyhydrate systems

    CERN Document Server

    Sucharev, Yuri I

    2008-01-01

    The present monograph is the first systematic study of the non-linear characteristic of gel oxy-hydrate systems involving d- and f- elements. These are the oxyhydrates of rare-earth elements and oxides - hydroxides of d- elements (zirconium, niobium, titanium, etc.) The non-linearity of these gel systems introduces fundamental peculiarities into their structure and, consequently, their properties. The polymer-conformational diversity of energetically congenial gel fragments, which continu-ously transform under the effect of, for instance, system dissipation heat, is central to the au-thor's hy

  8. The presentation of explicit analytical solutions of a class of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Feng Jinshun; Guo Mingpu; Yuan Deyou

    2009-01-01

    In this paper, we introduce a function set Ω m . There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in Ω m . A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.

  9. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

  10. Nonlinear evolution of magnetic islands in a two fluid torus

    International Nuclear Information System (INIS)

    Sugiyama, L.E.; Park, W.

    1996-01-01

    A numerical model MH3D-T for the two fluid description of macroscopic evolution in a full three dimensional torus has been developed. Based on the perturbative drift ordering, generalized to arbitrary perturbation size, the model follows the full temperature evolution, including the thermal equilibration along the magnetic field. It contains the diamagnetic drifts, ion gyroviscous stress tensor, and the Hall term in Ohm's law. Electron inertia is neglected. The numerical model solves the same equations in a torus and in several simplified configurations. It has been benchmarked against the diamagnetic ω* i stabilization of the resistive m = 1, n = 1 reconnecting mode in a cylinder. The nonlinear evolution of resistive magnetic islands with m,n ≠ 1,1 in a cylinder is found to agree with previous analytic and reduced-torus results, which show that the diamagnetic rotation vanishes early in the island evolution and the saturated island size is determined by the same external driving factor Δ' as in MHD. The two fluid evolution in a full torus, however, differs from that in a cylinder and from the resistive MHD evolution. The poloidal rotation velocity undergoes a degree of poloidal momentum damping in the torus, even without neoclassical effects. The two fluid magnetic island grows faster, nonlinearly, than the resistive MHD island, and also couples different toroidal harmonics more effectively. Plasma compressibility and processes operating along the magnetic field play a much more important role than in MHD or in simple geometry. The two fluid model contains all the important neoclassical fluid effects except for the b circ ∇ circ Π parallelj viscous force terms. The addition of these terms is in progress

  11. Exactly and completely integrable nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Leznov, A.N.; Savel'ev, M.V.

    1987-01-01

    The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

  12. Lectures on nonlinear evolution equations initial value problems

    CERN Document Server

    Racke, Reinhard

    2015-01-01

    This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

  13. Empirical Differential Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Kawano, Yu; Scherpen, Jacquelien M.A.; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri

    In this paper, we consider empirical balancing of nonlinear systems by using its prolonged system, which consists of the original nonlinear system and its variational system. For the prolonged system, we define differential reachability and observability Gramians, which are matrix valued functions

  14. The non-linear evolution of edge localized modes

    International Nuclear Information System (INIS)

    Wenninger, Ronald

    2013-01-01

    Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal

  15. The non-linear evolution of edge localized modes

    Energy Technology Data Exchange (ETDEWEB)

    Wenninger, Ronald

    2013-01-09

    Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal

  16. Nonlinear Waves in Complex Systems

    DEFF Research Database (Denmark)

    2007-01-01

    The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...

  17. Discontinuity and complexity in nonlinear physical systems

    CERN Document Server

    Baleanu, Dumitru; Luo, Albert

    2014-01-01

    This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....

  18. Stability analysis of nonlinear systems with slope restricted nonlinearities.

    Science.gov (United States)

    Liu, Xian; Du, Jiajia; Gao, Qing

    2014-01-01

    The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

  19. Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

    Directory of Open Access Journals (Sweden)

    Xian Liu

    2014-01-01

    Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

  20. Symbolic computation of exact solutions for a nonlinear evolution equation

    International Nuclear Information System (INIS)

    Liu Yinping; Li Zhibin; Wang Kuncheng

    2007-01-01

    In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here

  1. Differential Evolution-Based PID Control of Nonlinear Full-Car Electrohydraulic Suspensions

    Directory of Open Access Journals (Sweden)

    Jimoh O. Pedro

    2013-01-01

    Full Text Available This paper presents a differential-evolution- (DE- optimized, independent multiloop proportional-integral-derivative (PID controller design for full-car nonlinear, electrohydraulic suspension systems. The multiloop PID control stabilises the actuator via force feedback and also improves the system performance. Controller gains are computed using manual tuning and through DE optimization to minimise a performance index, which addresses suspension travel, road holding, vehicle handling, ride comfort, and power consumption constraints. Simulation results showed superior performance of the DE-optimized PID-controlled active vehicle suspension system (AVSS over the manually tuned PID-controlled AVSS and the passive vehicle suspension system (PVSS.

  2. Nonlinear evolution of f(R) cosmologies. II. Power spectrum

    International Nuclear Information System (INIS)

    Oyaizu, Hiroaki; Hu, Wayne; Lima, Marcos

    2008-01-01

    We carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances the force of gravity below the inverse mass or Compton scale of the scalar. The simulations exhibit the so-called chameleon mechanism, necessary for satisfying local constraints on gravity, where this scale depends on environment, in particular, the depth of the local gravitational potential. We find that the chameleon mechanism can substantially suppress the enhancement of power spectrum in the nonlinear regime if the background field value is comparable to or smaller than the depth of the gravitational potentials of typical structures. Nonetheless power spectrum enhancements at intermediate scales remain at a measurable level for models even when the expansion history is indistinguishable from a cosmological constant, cold dark matter model. Simple scaling relations that take the linear power spectrum into a nonlinear spectrum fail to capture the modifications of f(R) due to the change in collapsed structures, the chameleon mechanism, and the time evolution of the modifications.

  3. Positive real balancing for nonlinear systems

    NARCIS (Netherlands)

    Ionescu, Tudor C.; Scherpen, Jacquelien M.A.; Ciuprina, G; Ioan, D

    2007-01-01

    We extend the positive real balancing procedure for passive linear systems to the nonlinear systems case. We show that, just like in the linear case, model reduction based on this technique preserves passivity.

  4. Non-linear Evolution of the Transverse Instability of Plane-Envelope Solitons

    DEFF Research Database (Denmark)

    Janssen, Peter A. E. M.; Juul Rasmussen, Jens

    1983-01-01

    The nonlinear evolution of the transverse instability of plane envelope soliton solutions of the nonlinear Schrödinger equation is investigated. For the case where the spatial derivatives in the two‐dimensional nonlinear Schrödinger equation are elliptic a critical transverse wavenumber is found...

  5. On Stabilization of Nonautonomous Nonlinear Systems

    International Nuclear Information System (INIS)

    Bogdanov, A. Yu.

    2008-01-01

    The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

  6. Advances and applications in nonlinear control systems

    CERN Document Server

    Volos, Christos

    2016-01-01

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

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

    Directory of Open Access Journals (Sweden)

    S. J. Sadati

    2010-01-01

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

  8. Measurement Model Nonlinearity in Estimation of Dynamical Systems

    Science.gov (United States)

    Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

    2012-06-01

    The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.

  9. Evolution of stellar systems

    International Nuclear Information System (INIS)

    Vader, P.

    1981-01-01

    The stellar systems of which the evolution will be considered in this thesis, are either galaxies, which contain about 10 11 stars, or binary systems, which consist of only two stars. It is seen that binary systems can give us some insight into the relative age of the nucleus of M31. The positive correlation between the metal content of a galaxy and its mass, first noted for elliptical galaxies, seems to be a general property of galaxies of all types. The observed increase of metallicity with galaxy mass is too large to be accounted for by differences in the evolutionary stage of galaxies. To explain the observed correlation it is proposed that a relatively larger proportion of massive stars is formed in more massive galaxies. The physical basis is that the formation of massive stars seems to be tied to the enhanced gas-dynamical activity in more massive galaxies. A specific aspect of the production of heavy elements by massive stars is investigated in some detail. In 1979 a cluster of 18 point X-ray sources within 400 pc of the centre of M31 was detected with the Einstein satellite. This is a remarkable result since no equivalent of this cluster has been observed in the nucleus of our own Galaxy, which otherwise is very similar to that of M31. An explanation for this phenomenon is proposed, suggesting that X-ray binaries are the products of the long-term evolution of nova systems. (Auth.)

  10. Soliton dynamics in periodic system with different nonlinear media

    International Nuclear Information System (INIS)

    Zabolotskij, A.A.

    2001-01-01

    To analyze pulse dynamics in the optical system consisting of periodic sequence of nonlinear media one uses a composition model covering a model of resonance interaction of light ultrashort pulse with energy transition of medium with regard to pumping of the upper level and quasi-integrable model describing propagation of light field in another medium with cubic nonlinearity and dispersion. One additionally takes account of losses and other types of interaction in the from of perturbation members. On the basis of the method of scattering back problem and perturbation theory one developed a simple method to study peculiarities of soliton evolution in such periodic system. Due to its application one managed to describe different modes of soliton evolution in such a system including chaotic dynamics [ru

  11. Nonlinear evolution of f(R) cosmologies. I. Methodology

    International Nuclear Information System (INIS)

    Oyaizu, Hiroaki

    2008-01-01

    We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f(R) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a nonlinear Poisson equation for the scalar degree of freedom introduced by the f(R) modifications. We detail the method to efficiently solve the nonlinear Poisson equation by using a Newton-Gauss-Seidel relaxation scheme coupled with the multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f(R) physics. In general, we find that the f(R) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ∼20% for large but observationally allowed f(R) modifications. A more detailed study of the nonlinear f(R) effects on the power spectrum are presented in a companion paper.

  12. The solution of a coupled system of nonlinear physical problems using the homotopy analysis method

    International Nuclear Information System (INIS)

    El-Wakil, S A; Abdou, M A

    2010-01-01

    In this article, the homotopy analysis method (HAM) has been applied to solve coupled nonlinear evolution equations in physics. The validity of this method has been successfully demonstrated by applying it to two nonlinear evolution equations, namely coupled nonlinear diffusion reaction equations and the (2+1)-dimensional Nizhnik-Novikov Veselov system. The results obtained by this method show good agreement with the ones obtained by other methods. The proposed method is a powerful and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiliary parameter that provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.

  13. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

    Directory of Open Access Journals (Sweden)

    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  14. Nonlinear PDEs a dynamical systems approach

    CERN Document Server

    Schneider, Guido

    2017-01-01

    This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced...

  15. Universal formats for nonlinear ordinary differential systems

    International Nuclear Information System (INIS)

    Kerner, E.H.

    1981-01-01

    It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ''Riccati systems,'' where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format

  16. Nonlinear and Complex Dynamics in Real Systems

    OpenAIRE

    William Barnett; Apostolos Serletis; Demitre Serletis

    2005-01-01

    This paper was produced for the El-Naschie Symposium on Nonlinear Dynamics in Shanghai in December 2005. In this paper we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems with nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could p...

  17. Nonlinear evolution of large-scale structure in the universe

    International Nuclear Information System (INIS)

    Frenk, C.S.; White, S.D.M.; Davis, M.

    1983-01-01

    Using N-body simulations we study the nonlinear development of primordial density perturbation in an Einstein--de Sitter universe. We compare the evolution of an initial distribution without small-scale density fluctuations to evolution from a random Poisson distribution. These initial conditions mimic the assumptions of the adiabatic and isothermal theories of galaxy formation. The large-scale structures which form in the two cases are markedly dissimilar. In particular, the correlation function xi(r) and the visual appearance of our adiabatic (or ''pancake'') models match better the observed distribution of galaxies. This distribution is characterized by large-scale filamentary structure. Because the pancake models do not evolve in a self-similar fashion, the slope of xi(r) steepens with time; as a result there is a unique epoch at which these models fit the galaxy observations. We find the ratio of cutoff length to correlation length at this time to be lambda/sub min//r 0 = 5.1; its expected value in a neutrino dominated universe is 4(Ωh) -1 (H 0 = 100h km s -1 Mpc -1 ). At early epochs these models predict a negligible amplitude for xi(r) and could explain the lack of measurable clustering in the Lyα absorption lines of high-redshift quasars. However, large-scale structure in our models collapses after z = 2. If this collapse precedes galaxy formation as in the usual pancake theory, galaxies formed uncomfortably recently. The extent of this problem may depend on the cosmological model used; the present series of experiments should be extended in the future to include models with Ω<1

  18. Adaptive PI Controller for a Nonlinear System

    Directory of Open Access Journals (Sweden)

    D. Rathikarani

    2009-10-01

    Full Text Available Most of the industrial processes are inherently nonlinear in their behaviour. Designs of controllers for these nonlinear processes are difficult, as they do not follow superposition theorem. Adaptive controller can change its behaviour in response to changes in the dynamics of the process and disturbances. Hence adaptive controller can be used to control nonlinear processes. Direct Model Reference Adaptive Control is a technique, in which a reference model involving the desired performances is specified. In the present work, a DMRAC is designed and implemented to achieve satisfactory control of a nonlinear system in all its local linear operating regions. The closed loop system is made BIBO stable by proper control techniques. The controller is designed through simulation in Matlab platform and is validated in real time by conducting experiments on the laboratory Air Flow Control System using the dSPACE interface.

  19. A procedure to construct exact solutions of nonlinear evolution ...

    Indian Academy of Sciences (India)

    Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30. ... computer science, directly searching for solutions of nonlinear differential equations has become more and ... Right after this pioneer work, this ...

  20. Nonlinear dynamical system approaches towards neural prosthesis

    International Nuclear Information System (INIS)

    Torikai, Hiroyuki; Hashimoto, Sho

    2011-01-01

    An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

  1. Augmented nonlinear differentiator design and application to nonlinear uncertain systems.

    Science.gov (United States)

    Shao, Xingling; Liu, Jun; Li, Jie; Cao, Huiliang; Shen, Chong; Zhang, Xiaoming

    2017-03-01

    In this paper, an augmented nonlinear differentiator (AND) based on sigmoid function is developed to calculate the noise-less time derivative under noisy measurement condition. The essential philosophy of proposed AND in achieving high attenuation of noise effect is established by expanding the signal dynamics with extra state variable representing the integrated noisy measurement, then with the integral of measurement as input, the augmented differentiator is formulated to improve the estimation quality. The prominent advantages of the present differentiation technique are: (i) better noise suppression ability can be achieved without appreciable delay; (ii) the improved methodology can be readily extended to construct augmented high-order differentiator to obtain multiple derivatives. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, the robust control problems of nonlinear uncertain systems, including a numerical example and a mass spring system, are addressed to demonstrate the effectiveness of AND in precisely estimating the disturbance and providing the unavailable differential estimate to implement output feedback based controller. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  2. Controller Design of Complex System Based on Nonlinear Strength

    Directory of Open Access Journals (Sweden)

    Rongjun Mu

    2015-01-01

    Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

  3. Parametric Identification of Nonlinear Dynamical Systems

    Science.gov (United States)

    Feeny, Brian

    2002-01-01

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

  4. A study of discrete nonlinear systems

    International Nuclear Information System (INIS)

    Dhillon, H.S.

    2001-04-01

    An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

  5. Time evolution of absorption process in nonlinear metallic photonic crystals

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Mahi R.; Hatef, Ali [Department of Physics and Astronomy, University of Western Ontario, London (Canada)

    2009-05-15

    The time evolution of the absorption coefficient in metallic photonic crystals has been studied numerically. These crystals are made from metallic spheres which are arranged periodically in air. The refractive index of the metallic spheres depends on the plasma frequency. Probe and pump fields are applied to monitor the absorption process. Ensembles of three-level particles are embedded in the crystal. Nanoparticles are interacting with the metallic crystals via the electron-photon interaction. It is found that when the resonance states lie away from the band edges system goes to transparent state. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  6. Resonant driving of a nonlinear Hamiltonian system

    International Nuclear Information System (INIS)

    Palmisano, Carlo; Gervino, Gianpiero; Balma, Massimo; Devona, Dorina; Wimberger, Sandro

    2013-01-01

    As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving force which consists of periodic pulses additionally modulated by a sinusoidal function. The main observables are the average increase of kinetic energy and of the action variable (of the non-driven system) with time. Applications of our scheme aim for driving high frequencies of a nonlinear system with a fixed modulation signal.

  7. Controlling chaotic systems via nonlinear feedback control

    International Nuclear Information System (INIS)

    Park, Ju H.

    2005-01-01

    In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived

  8. A hierarchy of systems of nonlinear equations

    International Nuclear Information System (INIS)

    Falkensteiner, P.; Grosse, H.

    1985-01-01

    Imposing isospectral invariance for the one-dimensional Dirac operator yields an infinite hierarchy of systems of chiral invariant nonlinear partial differential equations. The same system is obtained through a Lax pair construction and finally a formulation in terms of Kac-Moody generators is given. (Author)

  9. Fault detection for nonlinear systems - A standard problem approach

    DEFF Research Database (Denmark)

    Stoustrup, Jakob; Niemann, Hans Henrik

    1998-01-01

    The paper describes a general method for designing (nonlinear) fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension...

  10. Network science, nonlinear science and infrastructure systems

    CERN Document Server

    2007-01-01

    Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .

  11. Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

    International Nuclear Information System (INIS)

    Alvarez-Estrada, R.F.

    1979-01-01

    A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

  12. Nonlinear dynamics of fractional order Duffing system

    International Nuclear Information System (INIS)

    Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

    2015-01-01

    In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

  13. Accurate detection of hierarchical communities in complex networks based on nonlinear dynamical evolution

    Science.gov (United States)

    Zhuo, Zhao; Cai, Shi-Min; Tang, Ming; Lai, Ying-Cheng

    2018-04-01

    One of the most challenging problems in network science is to accurately detect communities at distinct hierarchical scales. Most existing methods are based on structural analysis and manipulation, which are NP-hard. We articulate an alternative, dynamical evolution-based approach to the problem. The basic principle is to computationally implement a nonlinear dynamical process on all nodes in the network with a general coupling scheme, creating a networked dynamical system. Under a proper system setting and with an adjustable control parameter, the community structure of the network would "come out" or emerge naturally from the dynamical evolution of the system. As the control parameter is systematically varied, the community hierarchies at different scales can be revealed. As a concrete example of this general principle, we exploit clustered synchronization as a dynamical mechanism through which the hierarchical community structure can be uncovered. In particular, for quite arbitrary choices of the nonlinear nodal dynamics and coupling scheme, decreasing the coupling parameter from the global synchronization regime, in which the dynamical states of all nodes are perfectly synchronized, can lead to a weaker type of synchronization organized as clusters. We demonstrate the existence of optimal choices of the coupling parameter for which the synchronization clusters encode accurate information about the hierarchical community structure of the network. We test and validate our method using a standard class of benchmark modular networks with two distinct hierarchies of communities and a number of empirical networks arising from the real world. Our method is computationally extremely efficient, eliminating completely the NP-hard difficulty associated with previous methods. The basic principle of exploiting dynamical evolution to uncover hidden community organizations at different scales represents a "game-change" type of approach to addressing the problem of community

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

    Indian Academy of Sciences (India)

    2013-12-01

    Dec 1, 2013 ... 1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong,. NSW 2522 ... the nonlinear phenomena as well as their further applications in the real-life situations, it is ... concentration gradient. Thus ...

  15. New travelling wave solutions for nonlinear stochastic evolution ...

    Indian Academy of Sciences (India)

    expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.

  16. Solitary wave solutions to nonlinear evolution equations in ...

    Indian Academy of Sciences (India)

    1Computer Engineering Technique Department, Al-Rafidain University College, Baghdad, ... applied to extract solutions are tan–cot method and functional variable approaches. ... Consider the nonlinear partial differential equation in the form.

  17. Phase Control in Nonlinear Systems

    Science.gov (United States)

    Zambrano, Samuel; Seoane, Jesús M.; Mariño, Inés P.; Sanjuán, Miguel A. F.; Meucci, Riccardo

    The following sections are included: * Introduction * Phase Control of Chaos * Description of the model * Numerical exploration of phase control of chaos * Experimental evidence of phase control of chaos * Phase Control of Intermittency in Dynamical Systems * Crisis-induced intermittency and its control * Experimental setup and implementation of the phase control scheme * Phase control of the laser in the pre-crisis regime * Phase control of the intermittency after the crisis * Phase control of the intermittency in the quadratic map * Phase Control of Escapes in Open Dynamical Systems * Control of open dynamical systems * Model description * Numerical simulations and heuristic arguments * Experimental implementation in an electronic circuit * Conclusions and Discussions * Acknowledgments * References

  18. Workshop on Nonlinear Phenomena in Complex Systems

    CERN Document Server

    1989-01-01

    This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.

  19. Periodic Solutions for Highly Nonlinear Oscillation Systems

    DEFF Research Database (Denmark)

    Ghadimi, M; Barari, Amin; Kaliji, H.D

    2012-01-01

    In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...

  20. Exploring Nonlinearities in Financial Systemic Risk

    NARCIS (Netherlands)

    Wolski, M.

    2013-01-01

    We propose a new methodology of assessing the effects of individual institution's risk on the others and on the system as a whole. We build upon the Conditional Value-at-Risk approach, however, we introduce the explicit Granger causal linkages and we account for possible nonlinearities in the

  1. Experimental chaos in nonlinear vibration isolation system

    International Nuclear Information System (INIS)

    Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

    2009-01-01

    The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

  2. Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method

    International Nuclear Information System (INIS)

    Fan Engui

    2002-01-01

    A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)

  3. A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium

    International Nuclear Information System (INIS)

    Beretta, G.P.

    1986-01-01

    This paper addresses a mathematical problem relevant to the question of nonequilibrium and irreversibility, namely, that of ''designing'' a general evolution equation capable of describing irreversible but conservative relaxtion towards equilibrium. The objective is to present an interesting mathematical solution to this design problem, namely, a new nonlinear evolution equation that satisfies a set of very stringent relevant requirements. Three different frameworks are defined from which the new equation could be adopted, with entirely different interpretations. Some useful well-known mathematics involving Gram determinants are presented and a nonlinear evolution equation is given which meets the stringent design specifications

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

    CERN Document Server

    Gharaibeh, Khaled M

    2011-01-01

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

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

    International Nuclear Information System (INIS)

    Hunter, N.F. Jr.

    1990-01-01

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

  6. Indirect learning control for nonlinear dynamical systems

    Science.gov (United States)

    Ryu, Yeong Soon; Longman, Richard W.

    1993-01-01

    In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

  7. Dynamic evolution characteristics of a fractional order hydropower station system

    Science.gov (United States)

    Gao, Xiang; Chen, Diyi; Yan, Donglin; Xu, Beibei; Wang, Xiangyu

    2018-01-01

    This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.

  8. A variational approach to nonlinear evolution equations in optics

    Indian Academy of Sciences (India)

    optics. D ANDERSON, M LISAK and A BERNTSON£. Department of Electromagnetics, Chalmers University of Technology, SE-41296 Göteborg, Sweden. £Ericsson Telcom ... Many works in nonlinear optics have made efficient ...... focusing dynamics of a laser beam (or a Bose–Einstein condensate) in a parabolic external.

  9. NONLINEAR EVOLUTION OF BEAM-PLASMA INSTABILITY IN INHOMOGENEOUS MEDIUM

    International Nuclear Information System (INIS)

    Ziebell, L. F.; Pavan, J.; Yoon, P. H.; Gaelzer, R.

    2011-01-01

    The problem of electron-beam propagation in inhomogeneous solar wind is intimately related to the solar type II and/or type III radio bursts. Many scientists have addressed this issue in the past by means of quasi-linear theory, but in order to fully characterize the nonlinear dynamics, one must employ weak-turbulence theory. Available numerical solutions of the weak-turbulence theory either rely on only one nonlinear process (either decay or scattering), or when both nonlinear terms are included, the inhomogeneity effect is generally ignored. The present paper reports the full solution of weak-turbulence theory that includes both decay and scattering processes, and also incorporating the effects of density gradient. It is found that the quasi-linear effect sufficiently accounts for the primary Langmuir waves, but to properly characterize the back-scattered Langmuir wave, which is important for eventual radiation generation, it is found that both nonlinear decay and scattering processes make comparable contributions. Such a finding may be important in the quantitative analysis of the plasma emission process with application to solar type II and/or type III radio bursts.

  10. Canonical structure of evolution equations with non-linear ...

    Indian Academy of Sciences (India)

    The dispersion produced is compensated by non-linear effects resulting in the formation of exponentially localized .... determining the values of Lagrange's multipliers αis. We postulate that a slightly .... c3 «w2x -v. (36). To include the effect of the secondary constraint c3 in the total Hamiltonian H we modify. (33) as. 104.

  11. Soliton solutions of some nonlinear evolution equations with time ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...

  12. Nonlinear dynamic macromodeling techniques for audio systems

    Science.gov (United States)

    Ogrodzki, Jan; Bieńkowski, Piotr

    2015-09-01

    This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

  13. Model reduction of systems with localized nonlinearities.

    Energy Technology Data Exchange (ETDEWEB)

    Segalman, Daniel Joseph

    2006-03-01

    An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.

  14. Evolution of ERP systems

    NARCIS (Netherlands)

    Wortmann, J.C.; Bititci, U.S.; Carrie, A.S.

    1998-01-01

    This paper describes the development of ERP systems over time. It explores both the functionality and the technology of ERP-systems. It explains the increased importance of ERP systems in practice. The paper also addresses the difficulties encountered in implementing ERP systems in real life. Modern

  15. Controllability of nonlinear delay oscillating systems

    Directory of Open Access Journals (Sweden)

    Chengbin Liang

    2017-05-01

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

  16. Jet-like long spike in nonlinear evolution of ablative Rayleigh-Taylor instability

    International Nuclear Information System (INIS)

    Ye Wenhua; He Xiantu; Wang Lifeng

    2010-01-01

    We report the formation of jet-like long spike in the nonlinear evolution of the ablative Rayleigh-Taylor instability (ARTI) experiments by numerical simulations. A preheating model κ(T) = κ SH [1 + f(T)], where κ SH is the Spitzer-Haerm (SH) electron conductivity and f(T) interprets the preheating tongue effect in the cold plasma ahead of the ablative front [Phys. Rev. E 65 (2002) 57401], is introduced in simulations. The simulation results of the nonlinear evolution of the ARTI are in general agreement with the experiment results. It is found that two factors, i.e., the suppressing of ablative Kelvin-Helmholtz instability (AKHI) and the heat flow cone in the spike tips, contribute to the formation of jet-like long spike in the nonlinear evolution of the ARTI. (authors)

  17. Exact solutions for nonlinear evolution equations using Exp-function method

    International Nuclear Information System (INIS)

    Bekir, Ahmet; Boz, Ahmet

    2008-01-01

    In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

  18. Application of Exp-function method for (2 + 1)-dimensional nonlinear evolution equations

    International Nuclear Information System (INIS)

    Bekir, Ahmet; Boz, Ahmet

    2009-01-01

    In this paper, the Exp-function method is used to construct solitary and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. (2 + 1)-dimensional breaking soliton (Calogero) equation, modified Zakharov-Kuznetsov and Konopelchenko-Dubrovsky equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.

  19. An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2016-06-01

    Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

  20. Response and reliability analysis of nonlinear uncertain dynamical structures by the probability density evolution method

    DEFF Research Database (Denmark)

    Nielsen, Søren R. K.; Peng, Yongbo; Sichani, Mahdi Teimouri

    2016-01-01

    The paper deals with the response and reliability analysis of hysteretic or geometric nonlinear uncertain dynamical systems of arbitrary dimensionality driven by stochastic processes. The approach is based on the probability density evolution method proposed by Li and Chen (Stochastic dynamics...... of structures, 1st edn. Wiley, London, 2009; Probab Eng Mech 20(1):33–44, 2005), which circumvents the dimensional curse of traditional methods for the determination of non-stationary probability densities based on Markov process assumptions and the numerical solution of the related Fokker–Planck and Kolmogorov......–Feller equations. The main obstacle of the method is that a multi-dimensional convolution integral needs to be carried out over the sample space of a set of basic random variables, for which reason the number of these need to be relatively low. In order to handle this problem an approach is suggested, which...

  1. Network evolution by nonlinear preferential rewiring of edges

    Science.gov (United States)

    Xu, Xin-Jian; Hu, Xiao-Ming; Zhang, Li-Jie

    2011-06-01

    The mathematical framework for small-world networks proposed in a seminal paper by Watts and Strogatz sparked a widespread interest in modeling complex networks in the past decade. However, most of research contributing to static models is in contrast to real-world dynamic networks, such as social and biological networks, which are characterized by rearrangements of connections among agents. In this paper, we study dynamic networks evolved by nonlinear preferential rewiring of edges. The total numbers of vertices and edges of the network are conserved, but edges are continuously rewired according to the nonlinear preference. Assuming power-law kernels with exponents α and β, the network structures in stationary states display a distinct behavior, depending only on β. For β>1, the network is highly heterogeneous with the emergence of starlike structures. For β<1, the network is widely homogeneous with a typical connectivity. At β=1, the network is scale free with an exponential cutoff.

  2. Collective Dynamics of Nonlinear and Disordered Systems

    CERN Document Server

    Radons, G; Just, W

    2005-01-01

    Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

  3. Nonlinear evolution of tearing and coalescence instability with free boundary conditions

    International Nuclear Information System (INIS)

    Malara, F.; Veltri, P.; Carbone, V.

    1990-01-01

    The nonlinear evolution of a reconnection instability in a plane current sheet is described. In particular, the appearance of coalescence instability was studied, which follows the formation of a chain of magnetic islands due to the tearing instability. In order to describe realistically this phonemenon, the time evolution of all the unstable modes which are present in the spectrum at the same time is considered. Moreover, this study allows to investigate the turbulent energy cascade which forms owing to the nonlinear coupling between such modes. (R.P.) 9 refs.; 6 figs

  4. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

    International Nuclear Information System (INIS)

    Zhaqilao,

    2013-01-01

    A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed

  5. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn

    2013-12-06

    A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.

  6. Evolution of information systems

    DEFF Research Database (Denmark)

    Kristensen, Jan

    2000-01-01

    This article offers a dynamic view of continuously changes in a specific informational system illustrated through a case study in a small network company. Central aspects of the evolutionary process will be identified and framed in relation to the informational system change. It will be argued th...

  7. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

  8. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

  9. Evolution of semantic systems

    CERN Document Server

    Küppers, Bernd-Olaf; Artmann, Stefan

    2013-01-01

    Complex systems in nature and society make use of information for the development of their internal organization and the control of their functional mechanisms. Alongside technical aspects of storing, transmitting and processing information, the various semantic aspects of information, such as meaning, sense, reference and function, play a decisive part in the analysis of such systems.With the aim of fostering a better understanding of semantic systems from an evolutionary and multidisciplinary perspective, this volume collects contributions by philosophers and natural scientists, linguists, i

  10. Topological equivalence of nonlinear autonomous dynamical systems

    International Nuclear Information System (INIS)

    Nguyen Huynh Phan; Tran Van Nhung

    1995-12-01

    We show in this paper that the autonomous nonlinear dynamical system Σ(A,B,F): x' = Ax+Bu+F(x) is topologically equivalent to the linear dynamical system Σ(A,B,O): x' = Ax+Bu if the projection of A on the complement in R n of the controllable vectorial subspace is hyperbolic and if lipschitz constant of F is sufficiently small ( * ) and F(x) = 0 when parallel x parallel is sufficiently large ( ** ). In particular, if Σ(A,B,O) is controllable, it is topologically equivalent to Σ(A,B,F) when it is only that F satisfy ( ** ). (author). 18 refs

  11. Nonlinear system theory: another look at dependence.

    Science.gov (United States)

    Wu, Wei Biao

    2005-10-04

    Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.

  12. Tracking Control for Switched Cascade Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Xiaoxiao Dong

    2015-01-01

    Full Text Available The issue of H∞ output tracking for switched cascade nonlinear systems is discussed in this paper, where not all the linear parts of subsystems are stabilizable. The conditions of the solvability for the issue are given by virtue of the structural characteristics of the systems and the average dwell time method, in which the total activation time for stabilizable subsystems is longer than that for the unstabilizable subsystems. At last, a simulation example is used to demonstrate the validity and advantages of the proposed approach.

  13. Dynamics of Nonlinear Time-Delay Systems

    CERN Document Server

    Lakshmanan, Muthusamy

    2010-01-01

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

  14. Control of self-organizing nonlinear systems

    CERN Document Server

    Klapp, Sabine; Hövel, Philipp

    2016-01-01

    The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

  15. Evolution in close binary systems

    International Nuclear Information System (INIS)

    Yungel'son, L.R.; Masevich, A.G.

    1983-01-01

    Duality is the property most typical of stars. If one investigates how prevalent double stars are, making due allowance for selection effects, one finds that as many as 90 percent of all stars are paired. Contrary to tradition it is single stars that are out of the ordinary, and as will be shown presently even some of these may have been formed by coalescence of the members of binary systems. This review deals with the evolution of close binaries, defined as double-star systems whose evolution entails exchange of material between the two components

  16. Is DNA a nonlinear dynamical system where solitary conformational ...

    Indian Academy of Sciences (India)

    Unknown

    DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.

  17. Evolution of safeguards systems design

    International Nuclear Information System (INIS)

    Shipley, J.P.; Christensen, E.L.; Dietz, R.J.

    1979-01-01

    Safeguards systems play a vital detection and deterrence role in current nonproliferation policy. These safeguards systems have developed over the past three decades through the evolution of three essential components: the safeguards/process interface, safeguards performance criteria, and the technology necessary to support effective safeguards. This paper discusses the background and history of this evolutionary process, its major developments and status, and the future direction of safeguards system design

  18. On nonlinear evolution variational inequalities involving variable exponent

    Directory of Open Access Journals (Sweden)

    Mingqi Xiang

    2013-12-01

    Full Text Available In this paper, we discuss a class of quasilinear evolution variational inequalities with variable exponent growth conditions in a generalized Sobolev space. We obtain the existence of weak solutions by means of penalty method. Moreover, we study the extinction properties of weak solutions to parabolic inequalities and provide a sufficient condition that makes the weak solutions vanish in a finite time. The existence of global attractors for weak solutions is also obtained via the theories of multi-valued semiflow.

  19. Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter.

    Science.gov (United States)

    Laudyn, Urszula A; Jung, Paweł S; Zegadło, Krzysztof B; Karpierz, Miroslaw A; Assanto, Gaetano

    2014-11-15

    We demonstrate the evolution of higher order one-dimensional guided modes into two-dimensional solitary waves in a reorientational medium. The observations, carried out at two different wavelengths in chiral nematic liquid crystals, are in good agreement with a simple nonlocal nonlinear model.

  20. Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma

    Science.gov (United States)

    Vasquez, Bernard J.

    1993-01-01

    The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.

  1. Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

    International Nuclear Information System (INIS)

    Ebaid, A.

    2007-01-01

    Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method

  2. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2014-01-01

    Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

  3. A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

    Science.gov (United States)

    Motsa, S S; Magagula, V M; Sibanda, P

    2014-01-01

    This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

  4. Seismic analysis of a nonlinear airlock system

    International Nuclear Information System (INIS)

    Huang, S.N.

    1983-01-01

    The containment equipment airlock door of the Fast Flux Test Facility utilizes screw-type actuators as a push-pull mechanism for closing and opening operations. Special design features were used to protect these actuators from pressure differential loading. These made the door behave as a nonlinear system during a seismic event. Seismic analyses, utilizing the time history method, were conducted to determine the seismic loads on these scew-type actuators. Several sizes of actuators were examined. Procedures for determining the final optimum design are discussed in detail

  5. An efficient control algorithm for nonlinear systems

    International Nuclear Information System (INIS)

    Sinha, S.

    1990-12-01

    We suggest a scheme to step up the efficiency of a recently proposed adaptive control algorithm, which is remarkably effective for regulating nonlinear systems. The technique involves monitoring of the ''stiffness of control'' to get maximum gain while maintaining a predetermined accuracy. The success of the procedure is demonstrated for the case of the logistic map, where we show that the improvement in performance is often factors of tens, and for small control stiffness, even factors of hundreds. (author). 4 refs, 1 fig., 1 tab

  6. Localized excitations in a nonlinearly coupled magnetic drift wave-zonal flow system

    International Nuclear Information System (INIS)

    Shukla, Nitin; Shukla, P.K.

    2010-01-01

    We consider the amplitude modulation of the magnetic drift wave (MDW) by zonal flows (ZFs) in a nonuniform magnetoplasma. For this purpose, we use the two-fluid model to derive a nonlinear Schroedinger equation for the amplitude modulated MDWs in the presence of the ZF potential, and an evolution equation for the ZF potential which is reinforced by the nonlinear Lorentz force of the MDWs. Our nonlinearly coupled MDW-ZFs system of equations admits stationary solutions in the form of a localized MDW envelope and a shock-like ZF potential profile.

  7. Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

    International Nuclear Information System (INIS)

    Feng Qing-Hua; Zhang Yao-Ming; Meng Fan-Wei

    2011-01-01

    In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. (general)

  8. Impulse position control algorithms for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Sesekin, A. N., E-mail: sesekin@list.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation); Nepp, A. N., E-mail: anepp@urfu.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)

    2015-11-30

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  9. Impulse position control algorithms for nonlinear systems

    Science.gov (United States)

    Sesekin, A. N.; Nepp, A. N.

    2015-11-01

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  10. MPPT for Photovoltaic System Using Nonlinear Controller

    Directory of Open Access Journals (Sweden)

    Ramsha Iftikhar

    2018-01-01

    Full Text Available Photovoltaic (PV system generates energy that varies with the variation in environmental conditions such as temperature and solar radiation. To cope up with the ever increasing demand of energy, the PV system must operate at maximum power point (MPP, which changes with load as well as weather conditions. This paper proposes a nonlinear backstepping controller to harvest maximum power from a PV array using DC-DC buck converter. A regression plane is formulated after collecting the data of the PV array from its characteristic curves to provide the reference voltage to track MPP. Asymptotic stability of the system is proved using Lyapunov stability criteria. The simulation results validate the rapid tracking and efficient performance of the controller. For further validation of the results, it also provides a comparison of the proposed controller with conventional perturb and observe (P&O and fuzzy logic-based controller (FLBC under abrupt changes in environmental conditions.

  11. Deterministic nonlinear systems a short course

    CERN Document Server

    Anishchenko, Vadim S; Strelkova, Galina I

    2014-01-01

    This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems.  This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.

  12. Bifurcation methods of dynamical systems for handling nonlinear ...

    Indian Academy of Sciences (India)

    physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.

  13. Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains

    Energy Technology Data Exchange (ETDEWEB)

    Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk [Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)

    2017-10-01

    Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.

  14. Nonlinear dynamic analysis of flexible multibody systems

    Science.gov (United States)

    Bauchau, Olivier A.; Kang, Nam Kook

    1991-01-01

    Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

  15. Traveling solitary wave solutions to evolution equations with nonlinear terms of any order

    International Nuclear Information System (INIS)

    Feng Zhaosheng

    2003-01-01

    Many physical phenomena in one- or higher-dimensional space can be described by nonlinear evolution equations, which can be reduced to ordinary differential equations such as the Lienard equation. Thus, to study those ordinary differential equations is of significance not only in mathematics itself, but also in physics. In this paper, a kind of explicit exact solutions to the Lienard equation is obtained. The applications of the solutions to the nonlinear RR-equation and the compound KdV-type equation are presented, which extend the results obtained in the previous literature

  16. The Relationship between Nonconservative Schemes and Initial Values of Nonlinear Evolution Equations

    Institute of Scientific and Technical Information of China (English)

    林万涛

    2004-01-01

    For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given.Based on numerical tests, the relationship between the nonlinear computational stability and the construction of difference schemes, as well as the form of initial values, is further discussed. It is proved through both theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of nonconservative schemes is decided by the form of initial values.

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

    International Nuclear Information System (INIS)

    Yu Jiali; Yi Zhang; Zhang Lei

    2009-01-01

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

  18. Applications of Nonlinear Dynamics Model and Design of Complex Systems

    CERN Document Server

    In, Visarath; Palacios, Antonio

    2009-01-01

    This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

  19. Symplectic and Hamiltonian structures of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Dorfman, I.Y.

    1993-01-01

    A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field

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

    African Journals Online (AJOL)

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

  1. Expert system for accelerator single-freedom nonlinear components

    International Nuclear Information System (INIS)

    Wang Sheng; Xie Xi; Liu Chunliang

    1995-01-01

    An expert system by Arity Prolog is developed for accelerator single-freedom nonlinear components. It automatically yields any order approximate analytical solutions for various accelerator single-freedom nonlinear components. As an example, the eighth order approximate analytical solution is derived by this expert system for a general accelerator single-freedom nonlinear component, showing that the design of the expert system is successful

  2. Distributed Fault Detection for a Class of Nonlinear Stochastic Systems

    Directory of Open Access Journals (Sweden)

    Bingyong Yan

    2014-01-01

    Full Text Available A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs. Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.

  3. Computational Models for Nonlinear Aeroelastic Systems, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...

  4. Nonlinear PI control of chaotic systems using singular perturbation theory

    International Nuclear Information System (INIS)

    Wang Jiang; Wang Jing; Li Huiyan

    2005-01-01

    In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

  5. Model Updating Nonlinear System Identification Toolbox, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...

  6. Bifurcations and Patterns in Nonlinear Dissipative Systems

    Energy Technology Data Exchange (ETDEWEB)

    Guenter Ahlers

    2005-05-27

    This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.

  7. A linear evolution for non-linear dynamics and correlations in realistic nuclei

    International Nuclear Information System (INIS)

    Levin, E.; Lublinsky, M.

    2004-01-01

    A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei. Our results are presented as three new equations. The first one is a linear equation for QCD generating functional (and for scattering amplitude) that sums the 'fan' diagrams. For the amplitude this equation is equivalent to the non-linear Balitsky-Kovchegov equation. The second equation is a generalization of the Balitsky-Kovchegov non-linear equation to interactions with realistic nuclei. It includes a new correlation parameter which incorporates, in a model-dependent way, correlations inside the nuclei. The third equation is a non-linear equation for QCD generating functional (and for scattering amplitude) that in addition to the 'fan' diagrams sums the Glauber-Mueller multiple rescatterings

  8. Nonlinear analysis of a reaction-diffusion system: Amplitude equations

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

    2012-10-15

    A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

  9. Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

    International Nuclear Information System (INIS)

    Niu Yu-Jun; Pei Bing-Nan; Wang Xing-Yuan

    2012-01-01

    We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor. (general)

  10. Nonlinear dynamics of quadratically cubic systems

    International Nuclear Information System (INIS)

    Rudenko, O V

    2013-01-01

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

  11. Analysis and classification of nonlinear dispersive evolution equations in the potential representation

    International Nuclear Information System (INIS)

    Eichmann, U.A.; Draayer, J.P.; Ludu, A.

    2002-01-01

    A potential representation for the subset of travelling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves reduction of a third-order partial differential equation to a first-order ordinary differential equation. The potential representation allows us to deduce certain properties of the solutions without the actual need to solve the underlying evolution equation. In particular, the paper deals with the so-called K(n, m) equations. Starting from their respective potential representations it is shown that these equations can be classified according to a simple point transformation. As a result, e.g., all equations with linear dispersion join the same equivalence class with the Korteweg-deVries equation being its representative, and all soliton solutions of higher order nonlinear equations are thus equivalent to the KdV soliton. Certain equations with both linear and quadratic dispersions can also be treated within this equivalence class. (author)

  12. Evolution of nonlinear perturbations inside Einstein-Yang-Mills black holes

    International Nuclear Information System (INIS)

    Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M.

    1998-01-01

    We present our results on numerical study of evolution of nonlinear perturbations inside spherically symmetric black holes in the SU(2) Einstein-Yang-Mills (EYM) theory. Recent developments demonstrate a new type of the behaviour of the metric for EYM black hole interiors; the generic metric exhibits an infinitely oscillating approach to the singularity, which is a spacelike but not of the mixmaster type. The evolution of various types of spherically symmetric perturbations, propagating from the internal vicinity of the external horizon towards the singularity is investigated in a self-consistent way using an adaptive numerical algorithm. The obtained results give strong numerical evidence in favor of nonlinear stability of the generic EYM black hole interiors. Alternatively, the EYM black hole interiors of S (schwarzschild)-type, which form only a zero measure subset in the space of all internal solutions are found to be unstable and transform to the generic type as perturbations are developed

  13. Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

    DEFF Research Database (Denmark)

    Eldeberky, Y.; Madsen, Per A.

    1999-01-01

    and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

  14. Spatial nonlinearities: Cascading effects in the earth system

    Science.gov (United States)

    Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

    2006-01-01

    Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

  15. Three-dimensional, nonlinear evolution of the Rayleigh--Taylor instability of a thin layer

    International Nuclear Information System (INIS)

    Manheimer, W.; Colombant, D.; Ott, E.

    1984-01-01

    A numerical simulation scheme is developed to examine the nonlinear evolution of the Rayleigh--Taylor instability of a thin sheet in three dimensions. It is shown that the erosion of mass at the top of the bubble is approximately as described by two-dimensional simulations. However, mass is lost into spikes more slowly in three-dimensional than in two-dimensional simulations

  16. Forward-backward equations for nonlinear propagation in axially invariant optical systems

    International Nuclear Information System (INIS)

    Ferrando, Albert; Zacares, Mario; Fernandez de Cordoba, Pedro; Binosi, Daniele; Montero, Alvaro

    2005-01-01

    We present a general framework to deal with forward and backward components of the electromagnetic field in axially invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components, explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these equations inherently incorporate spatiotemporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and nonparaxial evolution of spatial structures are analyzed as examples

  17. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    Science.gov (United States)

    Xiong, G. Z.; Wang, L.; Li, X. Q.; Liu, H. F.; Tang, C. J.; Huang, J.; Zhang, X.; Wang, X. Q.

    2017-06-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet-Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs.

  18. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    International Nuclear Information System (INIS)

    Xiong, G Z; Liu, H F; Huang, J; Wang, X Q; Wang, L; Li, X Q; Tang, C J; Zhang, X

    2017-01-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet–Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs. (paper)

  19. From Hamiltonian chaos to complex systems a nonlinear physics approach

    CERN Document Server

    Leonetti, Marc

    2013-01-01

    From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of  research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...

  20. Frequency domain performance analysis of nonlinearly controlled motion systems

    NARCIS (Netherlands)

    Pavlov, A.V.; Wouw, van de N.; Pogromski, A.Y.; Heertjes, M.F.; Nijmeijer, H.

    2007-01-01

    At the heart of the performance analysis of linear motion control systems lie essential frequency domain characteristics such as sensitivity and complementary sensitivity functions. For a class of nonlinear motion control systems called convergent systems, generalized versions of these sensitivity

  1. Noninteracting control of nonlinear systems based on relaxed control

    NARCIS (Netherlands)

    Jayawardhana, B.

    2010-01-01

    In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to

  2. New developments in state estimation for Nonlinear Systems

    DEFF Research Database (Denmark)

    Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole

    2000-01-01

    Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a mult......-known estimators, such as the extended Kalman filter (EKF) and its higher-order relatives, in most practical applications....

  3. Model reduction of nonlinear systems subject to input disturbances

    KAUST Repository

    Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2017-01-01

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

  4. Radio Evolution of Supernova Remnants Including Nonlinear Particle Acceleration: Insights from Hydrodynamic Simulations

    Science.gov (United States)

    Pavlović, Marko Z.; Urošević, Dejan; Arbutina, Bojan; Orlando, Salvatore; Maxted, Nigel; Filipović, Miroslav D.

    2018-01-01

    We present a model for the radio evolution of supernova remnants (SNRs) obtained by using three-dimensional hydrodynamic simulations coupled with nonlinear kinetic theory of cosmic-ray (CR) acceleration in SNRs. We model the radio evolution of SNRs on a global level by performing simulations for a wide range of the relevant physical parameters, such as the ambient density, supernova (SN) explosion energy, acceleration efficiency, and magnetic field amplification (MFA) efficiency. We attribute the observed spread of radio surface brightnesses for corresponding SNR diameters to the spread of these parameters. In addition to our simulations of Type Ia SNRs, we also considered SNR radio evolution in denser, nonuniform circumstellar environments modified by the progenitor star wind. These simulations start with the mass of the ejecta substantially higher than in the case of a Type Ia SN and presumably lower shock speed. The magnetic field is understandably seen as very important for the radio evolution of SNRs. In terms of MFA, we include both resonant and nonresonant modes in our large-scale simulations by implementing models obtained from first-principles, particle-in-cell simulations and nonlinear magnetohydrodynamical simulations. We test the quality and reliability of our models on a sample consisting of Galactic and extragalactic SNRs. Our simulations give Σ ‑ D slopes between ‑4 and ‑6 for the full Sedov regime. Recent empirical slopes obtained for the Galactic samples are around ‑5, while those for the extragalactic samples are around ‑4.

  5. Model reduction of nonlinear systems subject to input disturbances

    KAUST Repository

    Ndoye, Ibrahima

    2017-07-10

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

  6. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  7. Eigenvalue problem and nonlinear evolution of kink modes in a toroidal plasma

    International Nuclear Information System (INIS)

    Ogino, T.; Takeda, S.; Sanuki, H.; Kamimura, T.

    1979-04-01

    The internal kink modes of a cylindrical plasma are investigated by a linear eigen value problem and their nonlinear evolution is studied by 3-dimensional MHD simulation based on the rectangular column model under the fixed boundary condition. The growth rates in two cases, namely uniform and diffused current profiles are analyzed in detail, which agree with the analytical estimation by Shafranov. The time evolution of the m = 1 mode showed that q > 1 is satisfied at the relaxation time (q safety factor), a stable configuration like a horse shoe (a new equilibrium) was formed. Also, the time evolution of the pressure p for the m = 2 mode showed that a stable configuration like a pair of anchors was formed. (author)

  8. Population ecology, nonlinear dynamics, and social evolution. I. Associations among nonrelatives.

    Science.gov (United States)

    Avilés, Leticia; Abbot, Patrick; Cutter, Asher D

    2002-02-01

    Using an individual-based and genetically explicit simulation model, we explore the evolution of sociality within a population-ecology and nonlinear-dynamics framework. Assuming that individual fitness is a unimodal function of group size and that cooperation may carry a relative fitness cost, we consider the evolution of one-generation breeding associations among nonrelatives. We explore how parameters such as the intrinsic rate of growth and group and global carrying capacities may influence social evolution and how social evolution may, in turn, influence and be influenced by emerging group-level and population-wide dynamics. We find that group living and cooperation evolve under a wide range of parameter values, even when cooperation is costly and the interactions can be defined as altruistic. Greater levels of cooperation, however, did evolve when cooperation carried a low or no relative fitness cost. Larger group carrying capacities allowed the evolution of larger groups but also resulted in lower cooperative tendencies. When the intrinsic rate of growth was not too small and control of the global population size was density dependent, the evolution of large cooperative tendencies resulted in dynamically unstable groups and populations. These results are consistent with the existence and typical group sizes of organisms ranging from the pleometrotic ants to the colonial birds and the global population outbreaks and crashes characteristic of organisms such as the migratory locusts and the tree-killing bark beetles.

  9. Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

    International Nuclear Information System (INIS)

    Keanini, R.G.

    2011-01-01

    Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the

  10. Useful tools for non-linear systems: Several non-linear integral inequalities

    Czech Academy of Sciences Publication Activity Database

    Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

    2013-01-01

    Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

  11. Nonlinear evolution of the mode structure of ELMs in realistic ASDEX Upgrade geometry

    Energy Technology Data Exchange (ETDEWEB)

    Krebs, Isabel; Hoelzl, Matthias; Lackner, Karl; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Boltzmannstr. 2, Garching (Germany); Collaboration: The ASDEX Upgrade Team

    2013-07-01

    Edge-localized modes (ELMs) are edge instabilities in H-mode plasmas, which eject particles and energy. The suitability of the H-mode for future fusion reactors depends crucially on the exact ELM dynamics as they can damage plasma facing components if too large. We have simulated ELMs in ASDEX Upgrade geometry using the nonlinear MHD code JOREK. Emphasis was put on the mode structure evolution in the early ELM phase which is characterized by the exponential growth of the unstable toroidal Fourier harmonics followed by a phase of saturation. In the linear phase, toroidal harmonics grow independently, whereas at larger amplitudes, the nonlinear interaction between the toroidal harmonics influences their growth and structure. Prior to mode saturation, the evolution of the mode structure can be reproduced well by a simple quadratic mode-interaction model, which yields a possible explanation for the strong n=1 component of type-I ELMs observed in ASDEX Upgrade. In the linear phase of the simulations, intermediate toroidal mode numbers (n 6-14) are most unstable as predicted by the peeling-ballooning model. But non-linearly, the n=1 component becomes important due to an energy transfer from pairs of linearly dominant toroidal harmonics with neighboring mode numbers to the n=1. The latter thereby changes its spatial structure.

  12. Open system evolution and 'memory dressing'

    International Nuclear Information System (INIS)

    Knezevic, Irena; Ferry, David K.

    2004-01-01

    Due to recent advances in quantum information, as well as in mesoscopic and nanoscale physics, the interest in the theory of open systems and decoherence has significantly increased. In this paper, we present an interesting approach to solving a time-convolutionless equation of motion for the open system reduced density matrix beyond the limit of weak coupling with the environment. Our approach is based on identifying an effective, memory-containing interaction in the equations of motion for the representation submatrices of the evolution operator (these submatices are written in a special basis, adapted for the 'partial-trace-free' approach, in the system+environment Liouville space). We then identify the 'memory dressing', a quantity crucial for solving the equation of motion for the reduced density matrix, which separates the effective from the real physical interaction. The memory dressing obeys a self-contained nonlinear equation of motion, which we solve exactly. The solution can be represented in a diagrammatic fashion after introducing an 'information exchange propagator', a quantity that describes the transfer of information to and from the system, so the cumulative effect of the information exchange results in the memory dressing. In the case of weak system-environment coupling, we present the expansion of the reduced density matrix in terms of the physical interaction up to the third order. However, our approach is capable of going beyond the weak-coupling limit, and we show how short-time behavior of an open system can be analyzed for arbitrary coupling strength. We illustrate the approach with a simple numerical example of single-particle level broadening for a two-particle interacting system on short time scales. Furthermore, we point out a way to identify the structure of decoherence-free subspaces using the present approach

  13. Energy flow theory of nonlinear dynamical systems with applications

    CERN Document Server

    Xing, Jing Tang

    2015-01-01

    This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

  14. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    1978-01-01

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

  15. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

  16. XXIII International Conference on Nonlinear Dynamics of Electronic Systems

    CERN Document Server

    Stoop, Ruedi; Stramaglia, Sebastiano

    2017-01-01

    This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.

  17. Nonlinear closure relations theory for transport processes in nonequilibrium systems

    International Nuclear Information System (INIS)

    Sonnino, Giorgio

    2009-01-01

    A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ('Onsager') transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

  18. The spectral transform as a tool for solving nonlinear discrete evolution equations

    International Nuclear Information System (INIS)

    Levi, D.

    1979-01-01

    In this contribution we study nonlinear differential difference equations which became important to the description of an increasing number of problems in natural science. Difference equations arise for instance in the study of electrical networks, in statistical problems, in queueing problems, in ecological problems, as computer models for differential equations and as models for wave excitation in plasma or vibrations of particles in an anharmonic lattice. We shall first review the passages necessary to solve linear discrete evolution equations by the discrete Fourier transfrom, then, starting from the Zakharov-Shabat discretized eigenvalue, problem, we shall introduce the spectral transform. In the following part we obtain the correlation between the evolution of the potentials and scattering data through the Wronskian technique, giving at the same time many other properties as, for example, the Baecklund transformations. Finally we recover some of the important equations belonging to this class of nonlinear discrete evolution equations and extend the method to equations with n-dependent coefficients. (HJ)

  19. A new hierarchy of generalized derivative nonlinear Schroedinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system

    International Nuclear Information System (INIS)

    Yan, Z.; Zhang, H.

    2001-01-01

    In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed

  20. Observations of linear and nonlinear processes in the foreshock wave evolution

    Directory of Open Access Journals (Sweden)

    Y. Narita

    2007-07-01

    Full Text Available Waves in the foreshock region are studied on the basis of a hypothesis that the linear process first excites the waves and further wave-wave nonlinearities distribute scatter the energy of the primary waves into a number of daughter waves. To examine this wave evolution scenario, the dispersion relations, the wave number spectra of the magnetic field energy, and the dimensionless cross helicity are determined from the observations made by the four Cluster spacecraft. The results confirm that the linear process is the ion/ion right-hand resonant instability, but the wave-wave interactions are not clearly identified. We discuss various reasons why the test for the wave-wave nonlinearities fails, and conclude that the higher order statistics would provide a direct evidence for the wave coupling phenomena.

  1. Some applications of nonlinear diffusion to processing of dynamic evolution images

    International Nuclear Information System (INIS)

    Goltsov, Alexey N.; Nikishov, Sergey A.

    1997-01-01

    Model nonlinear diffusion equation with the most simple Landau-Ginzburg free energy functional was applied to locate boundaries between meaningful regions of low-level images. The method is oriented to processing images of objects that are a result of dynamic evolution: images of different organs and tissues obtained by radiography and NMR methods, electron microscope images of morphogenesis fields, etc. In the methods developed by us, parameters of the nonlinear diffusion model are chosen on the basis of the preliminary treatment of the images. The parameters of the Landau-Ginzburg free energy functional are extracted from the structure factor of the images. Owing to such a choice of the model parameters, the image to be processed is located in the vicinity of the steady-state of the diffusion equation. The suggested method allows one to separate distinct structures having specific space characteristics from the whole image. The method was applied to processing X-ray images of the lung

  2. Nonlinear evolution of single spike structure and vortex in Richtmeyer-Meshkov instability

    International Nuclear Information System (INIS)

    Fukuda, Yuko O.; Nishihara, Katsunobu; Okamoto, Masayo; Nagatomo, Hideo; Matsuoka, Chihiro; Ishizaki, Ryuichi; Sakagami, Hitoshi

    1999-01-01

    Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated for two dimensional case, and axial symmetric and non axial symmetric cases with the use of a three-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. Difference of nonlinear growth rate and double spiral structure among three cases is also discussed by visualization of simulation data. In a case that there is no slip-off of initial spike axis, vorticity ring is relatively stable, but phase rotation occurs. (author)

  3. Advanced nonlinear engine speed control systems

    DEFF Research Database (Denmark)

    Vesterholm, Thomas; Hendricks, Elbert

    1994-01-01

    Several subsidiary control problems have turned out to be important for improving driveability and fuel consumption in modern spark ignition (SI) engine cars. Among these are idle speed control and cruise control. In this paper the idle speed and cruise control problems will be treated as one......: accurately tracking of a desired engine speed in the presence of model uncertainties and severe load disturbances. This is accomplished by using advanced nonlinear control techniques such as input/output-linearization and sliding mode control. These techniques take advantage of a nonlinear model...... of the engine dynamics, a mean value engine model....

  4. Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

    DEFF Research Database (Denmark)

    Bayat, M.; Shahidi, M.; Barari, Amin

    2011-01-01

    approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...

  5. Discrete-time inverse optimal control for nonlinear systems

    CERN Document Server

    Sanchez, Edgar N

    2013-01-01

    Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

  6. Applications of equivalent linearization approaches to nonlinear piping systems

    International Nuclear Information System (INIS)

    Park, Y.; Hofmayer, C.; Chokshi, N.

    1997-01-01

    The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA's are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations

  7. Analysis and design of robust decentralized controllers for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Schoenwald, D.A.

    1993-07-01

    Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.

  8. Hadron–Quark Combustion as a Nonlinear, Dynamical System

    Directory of Open Access Journals (Sweden)

    Amir Ouyed

    2018-03-01

    Full Text Available The hadron–quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron–quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

  9. Hadron–Quark Combustion as a Nonlinear, Dynamical System

    Science.gov (United States)

    Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth

    2018-03-01

    The hadron-quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron-quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.

  10. Passivity Based Stabilization of Non-minimum Phase Nonlinear Systems

    Czech Academy of Sciences Publication Activity Database

    Travieso-Torres, J.C.; Duarte-Mermoud, M.A.; Zagalak, Petr

    2009-01-01

    Roč. 45, č. 3 (2009), s. 417-426 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear systems * stabilisation * passivity * state feedback Subject RIV: BC - Control Systems Theory Impact factor: 0.445, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-passivity based stabilization of non-minimum phase nonlinear systems.pdf

  11. The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Liu Chunping; Liu Xiaoping

    2004-01-01

    First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions

  12. Modelling of the nonlinear evolution of 2D waves and vortices in plasmas

    International Nuclear Information System (INIS)

    Taranov, V.B.

    1998-01-01

    In this report an antisymmetric lattice formed by standing waves of vorticity is considered. For small but finite amplitudes multiple-time-scale analysis is performed, higher harmonics generation and frequency shifts are evaluated analytically and critical amplitude for perturbation theory is determined. For amplitudes bigger than critical numerical simulations are carried out taking into account vortex nonlinearity, drift and dispersion effects. Numerical code is developed which allows to study long-term evolution of two-dimensional spatially periodic waves and vortex structures

  13. A class of periodic solutions of nonlinear wave and evolution equations

    International Nuclear Information System (INIS)

    Kashcheev, V.N.

    1987-01-01

    For the case of 1+1 dimensions a new heuristic method is proposed for deriving dels-similar solutions to nonlinear autonomous differential equations. If the differential function f is a polynomial, then: (i) in the case of even derivatives in f the solution is the ratio of two polynomials from the Weierstrass elliptic functions; (ii) in the case of any order derivatives in f the solution is the ratio of two polynomials from simple exponents. Numerous examples are given constructing such periodic solutions to the wave and evolution equations

  14. Nonlinear propagation in fusion laser systems

    International Nuclear Information System (INIS)

    Bliss, E.S.; Glass, A.J.; Glaze, J.A.

    1977-11-01

    This report was assembled to provide a brief review of the historical development of the study of self-focusing and nonlinear light propagation and its impact on the design of large, Nd-glass lasers for fusion research. No claim to completeness is made, but we feel that the enclosed summary does not miss many of the major developments in the field

  15. Linear vs non-linear QCD evolution: from HERA data to LHC phenomenology

    CERN Document Server

    Albacete, J L; Quiroga-Arias, P; Rojo, J

    2012-01-01

    The very precise combined HERA data provides a testing ground in which the relevance of novel QCD regimes, other than the successful linear DGLAP evolution, in small-x inclusive DIS data can be ascertained. We present a study of the dependence of the AAMQS fits, based on the running coupling BK non-linear evolution equations (rcBK), on the fitted dataset. This allows for the identification of the kinematical region where rcBK accurately describes the data, and thus for the determination of its applicability boundary. We compare the rcBK results with NNLO DGLAP fits, obtained with the NNPDF methodology with analogous kinematical cuts. Further, we explore the impact on LHC phenomenology of applying stringent kinematical cuts to the low-x HERA data in a DGLAP fit.

  16. Point source identification in nonlinear advection–diffusion–reaction systems

    International Nuclear Information System (INIS)

    Mamonov, A V; Tsai, Y-H R

    2013-01-01

    We consider a problem of identification of point sources in time-dependent advection–diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the nonlinearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements. (paper)

  17. Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

    International Nuclear Information System (INIS)

    Zhang Zhijie; Jiang Dongguang; Wang Wei

    2011-01-01

    Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)

  18. Model Updating Nonlinear System Identification Toolbox, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...

  19. Stabilization and Control Models of Systems With Hysteresis Nonlinearities

    Directory of Open Access Journals (Sweden)

    Mihail E. Semenov

    2012-05-01

    Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.

  20. Geometric Theory of Reduction of Nonlinear Control Systems

    Science.gov (United States)

    Elkin, V. I.

    2018-02-01

    The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

  1. Computational Models for Nonlinear Aeroelastic Systems, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...

  2. Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

    Science.gov (United States)

    Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

    2016-11-14

    In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

  3. Self-sustained solitons in systems with nonlinear damping

    International Nuclear Information System (INIS)

    Gonzalez, J.A.

    1993-05-01

    The existence and stability of kinks in systems with nonlinear damping are investigated. We discuss the mechanism of a bifurcation after which the kink becomes a non-stationary state. (author). 9 refs

  4. Optimal beamforming in MIMO systems with HPA nonlinearity

    KAUST Repository

    Qi, Jian

    2010-09-01

    In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

  5. Robust receding horizon control for networked and distributed nonlinear systems

    CERN Document Server

    Li, Huiping

    2017-01-01

    This book offers a comprehensive, easy-to-understand overview of receding-horizon control for nonlinear networks. It presents novel general strategies that can simultaneously handle general nonlinear dynamics, system constraints, and disturbances arising in networked and large-scale systems and which can be widely applied. These receding-horizon-control-based strategies can achieve sub-optimal control performance while ensuring closed-loop stability: a feature attractive to engineers. The authors address the problems of networked and distributed control step-by-step, gradually increasing the level of challenge presented. The book first introduces the state-feedback control problems of nonlinear networked systems and then studies output feedback control problems. For large-scale nonlinear systems, disturbance is considered first, then communication delay separately, and lastly the simultaneous combination of delays and disturbances. Each chapter of this easy-to-follow book not only proposes and analyzes novel ...

  6. Optimal beamforming in MIMO systems with HPA nonlinearity

    KAUST Repository

    Qi, Jian; Aissa, Sonia

    2010-01-01

    In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

  7. The nonlinear dynamics of a coupled fission system

    International Nuclear Information System (INIS)

    Bilanovic, Z.; Harms, A.A.

    1993-01-01

    The dynamic properties of a nonlinear and in situ vibrationally perturbed nuclear-to-thermal coupled neutron multiplying medium are examined. Some unique self-organizational temporal patterns appear in such fission systems and suggest a complex underlying dynamic. (Author)

  8. A numerical study of one-dimensional replicating patterns in reaction-diffusion systems with non-linear diffusion coefficients

    International Nuclear Information System (INIS)

    Ferreri, J. C.; Carmen, A. del

    1998-01-01

    A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs

  9. Robust stabilization of nonlinear systems: The LMI approach

    Directory of Open Access Journals (Sweden)

    Šiljak D. D.

    2000-01-01

    Full Text Available This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI. The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable. We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.

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

    International Nuclear Information System (INIS)

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

    2016-01-01

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

  11. Nonlinear physical systems spectral analysis, stability and bifurcations

    CERN Document Server

    Kirillov, Oleg N

    2013-01-01

    Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam

  12. Nonlinear dynamics of a coherent polariton-biexciton system

    International Nuclear Information System (INIS)

    Nguyen Trung Dan; Vo Tinh

    1994-08-01

    The nonlinear dynamics of a coherent interacting polariton-biexciton system in optically excited semiconductors is investigated. We consider the case when two macroscopically coherent modes - a lower branch polariton and a biexciton existing simultaneously in a direct-gap semiconductor. The conditions for exhibiting optical bistability in stationary regime are obtained. Numerical simulation for the nonlinear dynamics equations of the system is also carried out. (author). 16 refs, 4 figs

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

    Directory of Open Access Journals (Sweden)

    Jun Yan

    2013-01-01

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

  14. MINPACK-1, Subroutine Library for Nonlinear Equation System

    International Nuclear Information System (INIS)

    Garbow, Burton S.

    1984-01-01

    1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

  15. Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

    Science.gov (United States)

    Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.

    2018-03-01

    On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

  16. A novel algebraic procedure for solving non-linear evolution equations of higher order

    International Nuclear Information System (INIS)

    Huber, Alfred

    2007-01-01

    We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest

  17. Nonlinear evolution of the matter power spectrum in modified theories of gravity

    International Nuclear Information System (INIS)

    Koyama, Kazuya; Taruya, Atsushi; Hiramatsu, Takashi

    2009-01-01

    We present a formalism to calculate the nonlinear matter power spectrum in modified gravity models that explain the late-time acceleration of the Universe without dark energy. Any successful modified gravity models should contain a mechanism to recover general relativity (GR) on small scales in order to avoid the stringent constrains on deviations from GR at solar system scales. Based on our formalism, the quasi-nonlinear power spectrum in the Dvali-Gabadadze-Porratti braneworld models and f(R) gravity models are derived by taking into account the mechanism to recover GR properly. We also extrapolate our predictions to fully nonlinear scales using the parametrized post-Friedmann framework. In the Dvali-Gabadadze-Porratti and f(R) gravity models, the predicted nonlinear power spectrum is shown to reproduce N-body results. We find that the mechanism to recover GR suppresses the difference between the modified gravity models and dark energy models with the same expansion history, but the difference remains large at the weakly nonlinear regime in these models. Our formalism is applicable to a wide variety of modified gravity models and it is ready to use once consistent models for modified gravity are developed.

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

    Science.gov (United States)

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

    2017-10-31

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

  19. Nonlinear systems techniques for dynamical analysis and control

    CERN Document Server

    Lefeber, Erjen; Arteaga, Ines

    2017-01-01

    This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...

  20. Structure Learning in Stochastic Non-linear Dynamical Systems

    Science.gov (United States)

    Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.

    2005-12-01

    A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.

  1. ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

    KAUST Repository

    Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed

    2014-01-01

    In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown

  2. A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

    Directory of Open Access Journals (Sweden)

    S.H. Chen

    1996-01-01

    Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

  3. Nonlinear signal processing using neural networks: Prediction and system modelling

    Energy Technology Data Exchange (ETDEWEB)

    Lapedes, A.; Farber, R.

    1987-06-01

    The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

  4. Modelling Geomorphic Systems: Landscape Evolution

    OpenAIRE

    Valters, Declan

    2016-01-01

    Landscape evolution models (LEMs) present the geomorphologist with a means of investigating how landscapes evolve in response to external forcings, such as climate and tectonics, as well as internal process laws. LEMs typically incorporate a range of different geomorphic transport laws integrated in a way that simulates the evolution of a 3D terrain surface forward through time. The strengths of LEMs as research tools lie in their ability to rapidly test many different hypotheses of landscape...

  5. Parameter and Structure Inference for Nonlinear Dynamical Systems

    Science.gov (United States)

    Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

    2006-01-01

    A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

  6. Nonlinear Predictive Sliding Mode Control for Active Suspension System

    Directory of Open Access Journals (Sweden)

    Dazhuang Wang

    2018-01-01

    Full Text Available An active suspension system is important in meeting the requirements of the ride comfort and handling stability for vehicles. In this work, a nonlinear model of active suspension system and a corresponding nonlinear robust predictive sliding mode control are established for the control problem of active suspension. Firstly, a seven-degree-of-freedom active suspension model is established considering the nonlinear effects of springs and dampers; and secondly, the dynamic model is expanded in the time domain, and the corresponding predictive sliding mode control is established. The uncertainties in the controller are approximated by the fuzzy logic system, and the adaptive controller reduces the approximation error to increase the robustness of the control system. Finally, the simulation results show that the ride comfort and handling stability performance of the active suspension system is better than that of the passive suspension system and the Skyhook active suspension. Thus, the system can obviously improve the shock absorption performance of vehicles.

  7. An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules

    Directory of Open Access Journals (Sweden)

    Md. Nur Alam

    2017-11-01

    Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines

  8. A new extended H∞ filter for discrete nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    张永安; 周荻; 段广仁

    2004-01-01

    Nonlinear estimation problem is investigated in this paper. By extension of a linear H∞ estimation with corrector-predictor form to nonlinear cases, a new extended H∞ filter is proposed for time-varying discretetime nonlinear systems. The new filter has a simple observer structure based on a local linearization model, and can be viewed as a general case of the extended Kalman filter (EKF). An example demonstrates that the new filter with a suitable-chosen prescribed H∞ bound performs better than the EKF.

  9. Integrability of a system of two nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Zhukhunashvili, V.Z.

    1989-01-01

    In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants

  10. Stability properties of nonlinear dynamical systems and evolutionary stable states

    Energy Technology Data Exchange (ETDEWEB)

    Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)

    2017-03-18

    Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.

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

    Directory of Open Access Journals (Sweden)

    Yu Wang

    2014-01-01

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

  12. Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

    Directory of Open Access Journals (Sweden)

    S. L. Han

    2012-01-01

    Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

  13. Fault detection and fault-tolerant control for nonlinear systems

    CERN Document Server

    Li, Linlin

    2016-01-01

    Linlin Li addresses the analysis and design issues of observer-based FD and FTC for nonlinear systems. The author analyses the existence conditions for the nonlinear observer-based FD systems to gain a deeper insight into the construction of FD systems. Aided by the T-S fuzzy technique, she recommends different design schemes, among them the L_inf/L_2 type of FD systems. The derived FD and FTC approaches are verified by two benchmark processes. Contents Overview of FD and FTC Technology Configuration of Nonlinear Observer-Based FD Systems Design of L2 nonlinear Observer-Based FD Systems Design of Weighted Fuzzy Observer-Based FD Systems FTC Configurations for Nonlinear Systems< Application to Benchmark Processes Target Groups Researchers and students in the field of engineering with a focus on fault diagnosis and fault-tolerant control fields The Author Dr. Linlin Li completed her dissertation under the supervision of Prof. Steven X. Ding at the Faculty of Engineering, University of Duisburg-Essen, Germany...

  14. Mathematical Systems Theory : from Behaviors to Nonlinear Control

    CERN Document Server

    Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien

    2015-01-01

    This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...

  15. On nonequilibrium many-body systems III: nonlinear transport theory

    International Nuclear Information System (INIS)

    Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.

    1986-01-01

    A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt

  16. Nonlinear effects in evolution - an ab initio study: A model in which the classical theory of evolution occurs as a special case.

    Science.gov (United States)

    Clerc, Daryl G

    2016-07-21

    An ab initio approach was used to study the molecular-level interactions that connect gene-mutation to changes in an organism׳s phenotype. The study provides new insights into the evolutionary process and presents a simplification whereby changes in phenotypic properties may be studied in terms of the binding affinities of the chemical interactions affected by mutation, rather than by correlation to the genes. The study also reports the role that nonlinear effects play in the progression of organs, and how those effects relate to the classical theory of evolution. Results indicate that the classical theory of evolution occurs as a special case within the ab initio model - a case having two attributes. The first attribute: proteins and promoter regions are not shared among organs. The second attribute: continuous limiting behavior exists in the physical properties of organs as well as in the binding affinity of the associated chemical interactions, with respect to displacements in the chemical properties of proteins and promoter regions induced by mutation. Outside of the special case, second-order coupling contributions are significant and nonlinear effects play an important role, a result corroborated by analyses of published activity levels in binding and transactivation assays. Further, gradations in the state of perfection of an organ may be small or large depending on the type of mutation, and not necessarily closely-separated as maintained by the classical theory. Results also indicate that organs progress with varying degrees of interdependence, the likelihood of successful mutation decreases with increasing complexity of the affected chemical system, and differences between the ab initio model and the classical theory increase with increasing complexity of the organism. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

  17. Chaos synchronization of a new chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Zhang Qunjiao; Lu Junan

    2008-01-01

    This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

  18. Robust Nonlinear Control with Compensation Operator for a Peltier System

    Directory of Open Access Journals (Sweden)

    Sheng-Jun Wen

    2014-01-01

    Full Text Available Robust nonlinear control with compensation operator is presented for a Peltier actuated system, where the compensation operator is designed by using a predictive model on heat radiation. For the Peltier system, the heat radiation is related to the fourth power of temperature. So, the heat radiation is affected evidently by the temperature when it is high and temperature difference between the system and environment is large. A new nonlinear model with the heat radiation is set up for the system according to some thermal conduction laws. To ensure robust stability of the nonlinear system, operator based robust right coprime factorization design is considered. Also, a compensation operator based on a predictive model is proposed to cancel effect of the heat radiation, where the predictive model is set up by using radial basis kernel function based SVM (support vector machine method. Finally, simulation results are given to show the effectiveness of the proposed scheme.

  19. Nonlinear control for a class of hydraulic servo system.

    Science.gov (United States)

    Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong

    2004-11-01

    The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

  20. Rigorous Verification for the Solution of Nonlinear Interval System ...

    African Journals Online (AJOL)

    We survey a general method for solving nonlinear interval systems of equations. In particular, we paid special attention to the computational aspects of linear interval systems since the bulk of computations are done during the stage of computing outer estimation of the including linear interval systems. The height of our ...

  1. Synchronization of two different chaotic systems via nonlinear ...

    African Journals Online (AJOL)

    ADOWIE PERE

    ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.

  2. Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy

    OpenAIRE

    Neagu, Mircea

    2007-01-01

    The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.

  3. Lie symmetries for systems of evolution equations

    Science.gov (United States)

    Paliathanasis, Andronikos; Tsamparlis, Michael

    2018-01-01

    The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

  4. Effects of toroidal coupling on the non-linear evolution of tearing modes and on the stochastisation of the magnetic field topology in plasmas

    International Nuclear Information System (INIS)

    Edery, D.; Pellat, R.; Soule, J.L.

    1981-01-01

    The resistive MHD equations have been handled in toroidal geometry following the tokamak ordering, in order to obtain a simplified set of non-linear equations. This system of equations is compact, closed, consistent and exact to the first two orders in the expansion in the inverse aspect ratio. Studies of the non-linear evolution of tearing modes in the real geometry of tokamak discharges are now in progress, and quite significant results have been obtained from the numerical code REVE of Fontenay based on our above model. From the analytical results, strong linear coupling between neighbouring modes is expected as is demonstrated by the numerical results in the linear, and non-linear regimes. Moreover, coupling exhibits a stochastic structure of the magnetic field lines, the threshold of which is seen to be easily computed by a simple analytical criterion. (orig.)

  5. Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit

    International Nuclear Information System (INIS)

    Wang Jinzhi; Duan Zhisheng; Huang Lin

    2006-01-01

    In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method

  6. A nonlinear complementarity approach for the national energy modeling system

    International Nuclear Information System (INIS)

    Gabriel, S.A.; Kydes, A.S.

    1995-01-01

    The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP

  7. Nonlinear dynamic analysis of 2-DOF nonlinear vibration isolation floating raft systems with feedback control

    International Nuclear Information System (INIS)

    Li Yingli; Xu Daolin; Fu Yiming; Zhou Jiaxi

    2012-01-01

    In this paper, the average method is adopted to analysis dynamic characteristics of nonlinear vibration isolation floating raft system with feedback control. The analytic results show that the purposes of reducing amplitude of oscillation and complicating the motion can be achieved by adjusting properly the system parameters, exciting frequency and control gain. The conclusions can provide some available evidences for the design and improvement of both the passive and active control of the vibration isolation systems. By altering the exciting frequency and control gain, complex motion of the system can be obtained. Numerical simulations show the system exhibits period vibration, double period vibration and quasi-period motion.

  8. Incremental passivity and output regulation for switched nonlinear systems

    Science.gov (United States)

    Pang, Hongbo; Zhao, Jun

    2017-10-01

    This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.

  9. Decreasing the LHC impedance with a nonlinear collimation system

    CERN Document Server

    Resta-López, J; Zimmermann, F

    2007-01-01

    A two-stage nonlinear collimation system based on a pair of skew sextupoles is presented for the LHC.We show the details of the optics design and study the halo cleaning efficiency of such a system. This nonlinear collimation system would allow opening up collimator gaps, and thereby reduce the collimator impedance, which presently limits the LHC beam intensity. Assuming the nominal LHC beam at 7 TeV, the transverse coherent tune shifts of rigid-dipole coupled-bunch modes are computed for both the baseline linear collimation system and the proposed nonlinear one. In either case, the tune shifts of the most unstable modes are compared with the stability diagrams for Landau damping.

  10. Nonlinear dynamical system identification using unscented Kalman filter

    Science.gov (United States)

    Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan

    2016-11-01

    Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.

  11. Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression.

    Science.gov (United States)

    Ding, Bo; Fang, Huajing

    2017-05-01

    This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Nonlinear evolution dynamics of holographic superconductor model with scalar self-interaction

    Science.gov (United States)

    Li, Ran; Zi, Tieguang; Zhang, Hongbao

    2018-04-01

    We investigate the holographic superconductor model that is described by the Einstein-Maxwell theory with the self-interaction term λ |Ψ |4 of complex scalar field in asymptotic anti-de Sitter (AdS) spacetime. Below critical temperature Tc, the planar Reissner-Nordström-AdS black hole is unstable due to the near-horizon scalar condensation instability. We study the full nonlinear development of this instability by numerically solving the gravitational dynamics in the asymptotic AdS spacetime, and observe a dynamical process from the perturbed Reissner-Nordström-AdS black hole to a hairy black hole when the initial black hole temperature T process is then holographically dual to the dynamical superconducting phase transition process in the boundary theory. Furthermore, we also study the effect of the scalar self-interaction on time evolution of superconducting condensate operator, event and apparent horizon areas of the final hairy black hole.

  13. Seismic testing and analysis of a prototypic nonlinear piping system

    International Nuclear Information System (INIS)

    Barta, D.A.; Anderson, M.J.; Severud, L.K.

    1982-11-01

    A series of seismic tests and analyses of a nonlinear Fast Flux Test Facility (FFTF) prototypic piping system are described, and measured responses are compared with analytical predictions. The test loop was representative of a typical LMFBR insulated small bore piping system and it was supported from a rigid test frame by prototypic dead weight supports, mechanical snubbers and pipe clamps. Various piping support configurations were tested and analyzed to evaluate the effects of free play and other nonlinear stiffness characteristics on the piping system response

  14. Stability properties of a general class of nonlinear dynamical systems

    Science.gov (United States)

    Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

    2001-05-01

    We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

  15. Stability properties of a general class of nonlinear dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br

    2001-05-04

    We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)

  16. Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

    KAUST Repository

    Abdelkefi, Abdessattar

    2013-06-18

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

  17. Distributed control design for nonlinear output agreement in convergent systems

    NARCIS (Netherlands)

    Weitenberg, Erik; De Persis, Claudio

    2015-01-01

    This work studies the problem of output agreement in homogeneous networks of nonlinear dynamical systems under time-varying disturbances using controllers placed at the nodes of the networks. For the class of contractive systems, necessary and sufficient conditions for output agreement are derived,

  18. Linear time heteronymous damping in nonlinear parametric systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena; Houfek, Martin

    2016-01-01

    Roč. 40, 23-24 (2016), s. 10038-10051 ISSN 0307-904X Institutional support: RVO:61388998 Keywords : nonlinear dynamics of systems * parametric systems * time heteronymous damping * gears Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 2.350, year: 2016

  19. Nonlinear observer based phase synchronization of chaotic systems

    International Nuclear Information System (INIS)

    Meng Juan; Wang Xingyuan

    2007-01-01

    This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme

  20. On Similarity Invariance of Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, Jacquelien M.A.

    1995-01-01

    A previously obtained balancing method for nonlinear systems is investigated on similarity in variance by generalization of the observations on the similarity invariance of the linear balanced realization theory. For linear systems it is well known that the Hankel singular values are similarity

  1. A Simple Approach to Derive a Novel N-Soliton Solution for a (3+1)-Dimensional Nonlinear Evolution Equation

    International Nuclear Information System (INIS)

    Wu Jianping

    2010-01-01

    Based on the Hirota bilinear form, a simple approach without employing the standard perturbation technique, is presented for constructing a novel N-soliton solution for a (3+1)-dimensional nonlinear evolution equation. Moreover, the novel N-soliton solution is shown to have resonant behavior with the aid of Mathematica. (general)

  2. The relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Liu Chunping

    2003-01-01

    Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed

  3. Self-consistent simulations of nonlinear magnetohydrodynamics and profile evolution in stellarator configurations

    Energy Technology Data Exchange (ETDEWEB)

    Schlutt, M. G.; Hegna, C. C.; Sovinec, C. R. [University of Wisconsin-Madison, 1500 Engineering Dr., Madison, Wisconsin 53706 (United States); Held, E. D. [Utah State University, Logan, Utah 84322 (United States); Kruger, S. E. [Tech-X Corporation, 5621 Arapahoe Ave., Boulder, Colorado 80303 (United States)

    2013-05-15

    Self-consistent extended MHD framework is used to investigate nonlinear macroscopic dynamics of stellarator configurations. In these calculations, initial conditions are given by analytical 3-D vacuum solutions. Finite beta discharges in a straight stellarator are simulated. Vacuum magnetic fields are applied to produce stellarator-like rotational transform profiles with iota(0) ≤ 0.5 and iota(0) ≥ 0.5. The vacuum magnetic fields are either helically symmetric or spoiled by the presence of magnetic harmonics of incommensurate helicity. As heat is added to the system, pressure-driven instabilities are excited when a critical β is exceeded. These instabilities may grow to large amplitude and effectively terminate the discharge, or they may saturate nonlinearly as the configuration evolves. In all of these studies, anisotropic heat conduction is allowed with κ{sub ∥}/κ{sub ⊥}=10{sup 4}−10{sup 7}.

  4. Networked Predictive Control for Nonlinear Systems With Arbitrary Region Quantizers.

    Science.gov (United States)

    Yang, Hongjiu; Xu, Yang; Xia, Yuanqing; Zhang, Jinhui

    2017-04-06

    In this paper, networked predictive control is investigated for planar nonlinear systems with quantization by an extended state observer (ESO). The ESO is used not only to deal with nonlinear terms but also to generate predictive states for dealing with network-induced delays. Two arbitrary region quantizers are applied to take effective values of signals in forward channel and feedback channel, respectively. Based on a "zoom" strategy, sufficient conditions are given to guarantee stabilization of the closed-loop networked control system with quantization. A simulation example is proposed to exhibit advantages and availability of the results.

  5. Convergence criteria for systems of nonlinear elliptic partial differential equations

    International Nuclear Information System (INIS)

    Sharma, R.K.

    1986-01-01

    This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

  6. Multiscale analysis of nonlinear systems using computational homology

    Energy Technology Data Exchange (ETDEWEB)

    Konstantin Mischaikow; Michael Schatz; William Kalies; Thomas Wanner

    2010-05-24

    Characterization - We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. (6) Probabilistic Homology Validation - work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. (7) Computational Homology and Dynamics - Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. (8) Stress Networks in Polycrystals - we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. (9) Microstructure-Controlled Drug Release - This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. (10) Microstructure of Fuel Cells - we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.

  7. Multiscale analysis of nonlinear systems using computational homology

    Energy Technology Data Exchange (ETDEWEB)

    Konstantin Mischaikow, Rutgers University/Georgia Institute of Technology, Michael Schatz, Georgia Institute of Technology, William Kalies, Florida Atlantic University, Thomas Wanner,George Mason University

    2010-05-19

    Characterization - We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. (6) Probabilistic Homology Validation - work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. (7) Computational Homology and Dynamics - Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. (8) Stress Networks in Polycrystals - we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. (9) Microstructure-Controlled Drug Release - This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. (10) Microstructure of Fuel Cells - we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.

  8. Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations

    International Nuclear Information System (INIS)

    Qu Changzheng; Kang Jing

    2008-01-01

    In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.

  9. Chaos synchronizations of chaotic systems via active nonlinear control

    International Nuclear Information System (INIS)

    Huang, J; Xiao, T J

    2008-01-01

    This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective

  10. Accelerator-feasible N-body nonlinear integrable system

    Directory of Open Access Journals (Sweden)

    V. Danilov

    2014-12-01

    Full Text Available 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.

  11. Nonlinear dynamics non-integrable systems and chaotic dynamics

    CERN Document Server

    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.

  12. Asymptotic stabilization of nonlinear systems using state feedback

    International Nuclear Information System (INIS)

    D'Attellis, Carlos

    1990-01-01

    This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es

  13. Jump resonant frequency islands in nonlinear feedback control systems

    Science.gov (United States)

    Koenigsberg, W. D.; Dunn, J. C.

    1975-01-01

    A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.

  14. Methodology for global nonlinear analysis of nuclear systems

    International Nuclear Information System (INIS)

    Cacuci, D.G.; Cacuci, G.L.

    1987-01-01

    This paper outlines a general method for globally computing the crucial features of nonlinear problems: bifurcations, limit points, saddle points, extrema (maxima and minima); our method also yields the local sensitivities (i.e., first order derivatives) of the system's state variables (e.g., fluxes, power, temperatures, flows) at any point in the system's phase space. We also present an application of this method to the nonlinear BWR model discussed in Refs. 8 and 11. The most significant novel feature of our method is the recasting of a general mathematical problem comprising three aspects: (1) nonlinear constrained optimization, (2) sensitivity analysis, into a fixed point problem of the form F[u(s), λ(s)] = 0 whose global zeros and singular points are related to the special features (i.e., extrema, bifurcations, etc.) of the original problem

  15. Exact solutions for a system of nonlinear plasma fluid equations

    International Nuclear Information System (INIS)

    Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

    1991-04-01

    A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

  16. Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

    Directory of Open Access Journals (Sweden)

    Chuanjing Hou

    2015-01-01

    Full Text Available An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

  17. Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications

    OpenAIRE

    Hou, Chuanjing; Hu, Lisheng; Zhang, Yingwei

    2015-01-01

    An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective.

  18. The coupled nonlinear dynamics of a lift system

    Energy Technology Data Exchange (ETDEWEB)

    Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)

    2014-12-10

    Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.

  19. Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

    Directory of Open Access Journals (Sweden)

    Imran Talib

    2015-12-01

    Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

  20. Tracking Control of Nonlinear Mechanical Systems

    NARCIS (Netherlands)

    Lefeber, A.A.J.

    2000-01-01

    The subject of this thesis is the design of tracking controllers for certain classes of mechanical systems. The thesis consists of two parts. In the first part an accurate mathematical model of the mechanical system under consideration is assumed to be given. The goal is to follow a certain

  1. Stabilization of switched nonlinear systems with unstable modes

    CERN Document Server

    Yang, Hao; Cocquempot, Vincent

    2014-01-01

    This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...

  2. Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems

    International Nuclear Information System (INIS)

    Zhou Jin; Lu Junan; Wu Xiaoqun

    2007-01-01

    To date, there have been many results about unidirectionally coupled synchronization of chaotic systems. However, much less work is reported on bidirectionally-coupled synchronization. In this paper, we investigate the synchronization of two bidirectionally coupled Chen hyperchaotic systems, which are coupled linearly and nonlinearly respectively. Firstly, linearly coupled synchronization of two hyperchaotic Chen systems is investigated, and a theorem on how to choose the coupling coefficients are developed to guarantee the global asymptotical synchronization of two coupled hyperchaotic systems. Analysis shows that the choice of the coupling coefficients relies on the bound of the chaotic system. Secondly, the nonlinearly coupled synchronization is studied; a sufficient condition for the locally asymptotical synchronization is derived, which is independent of the bound of the hyperchaotic system. Finally, numerical simulations are included to verify the effectiveness and feasibility of the developed theorems

  3. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  4. Curve Evolution in Subspaces and Exploring the Metameric Class of Histogram of Gradient Orientation based Features using Nonlinear Projection Methods

    DEFF Research Database (Denmark)

    Tatu, Aditya Jayant

    This thesis deals with two unrelated issues, restricting curve evolution to subspaces and computing image patches in the equivalence class of Histogram of Gradient orientation based features using nonlinear projection methods. Curve evolution is a well known method used in various applications like...... tracking interfaces, active contour based segmentation methods and others. It can also be used to study shape spaces, as deforming a shape can be thought of as evolving its boundary curve. During curve evolution a curve traces out a path in the infinite dimensional space of curves. Due to application...... specific requirements like shape priors or a given data model, and due to limitations of the computer, the computed curve evolution forms a path in some finite dimensional subspace of the space of curves. We give methods to restrict the curve evolution to a finite dimensional linear or implicitly defined...

  5. PWL approximation of nonlinear dynamical systems, part I: structural stability

    International Nuclear Information System (INIS)

    Storace, M; De Feo, O

    2005-01-01

    This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)

  6. Reproduction of Economic Interests as a Nonlinear Dynamical System

    OpenAIRE

    Smiesova Viktoria L.

    2017-01-01

    The aim of the article is to define the system characteristics of reproduction of economic interests of actors, substantiate the possibility of its evolutionary and revolutionary development and the nonlinearity of its development in dynamics. The article justifies the main characteristics of the system of reproduction of economic interests. It is proved that in this system stability and variability are complementarily combined as integrated mechanisms of its development in statics and dynami...

  7. Chaos synchronization of a chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Park, Ju H.

    2005-01-01

    In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

  8. Integrable systems with quadratic nonlinearity in Fourier space

    International Nuclear Information System (INIS)

    Marikhin, V.G.

    2003-01-01

    The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed

  9. Nonlinear control system analysis and design with Maple

    NARCIS (Netherlands)

    Jager, de A.G.; Houstis, E.N.; Rice, J.R.

    1992-01-01

    For the analysis and design of nonlinear control systems non-numerical methods are available. The required analytical computations are mostly too tedious to be done error free in a reasonable time by hand, so the use of symbolic computation programs can be of advantage. To show that the symbolic

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

    African Journals Online (AJOL)

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

  11. Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations

    NARCIS (Netherlands)

    Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der

    Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general

  12. Nonlinear dynamics of a parametrically driven sine-Gordon system

    DEFF Research Database (Denmark)

    Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm

    1993-01-01

    We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...

  13. Relative controllability of nonlinear neutral systems with distributed ...

    African Journals Online (AJOL)

    In this paper we study the relative controllability of nonlinear neutral system with distributed and multiple lumped time varying delays in control. Using Schauder's fixed point theorem sufficient conditions for relative controllability in a given time interval are formulated and proved. Journal of the Nigerian Association of ...

  14. Attractors for a class of doubly nonlinear parabolic systems

    Directory of Open Access Journals (Sweden)

    Hamid El Ouardi

    2006-03-01

    Full Text Available In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in $\\left[ L^{\\infty }(\\Omega \\right] ^{2}$ and ${\\prod_{i=1}^{2}}{B_{\\infty }^{1+\\sigma_{i},p_{i}}( \\Omega } $.

  15. Preliminary Test for Nonlinear Input Output Relations in SISO Systems

    DEFF Research Database (Denmark)

    Knudsen, Torben

    2000-01-01

    This paper discusses and develops preliminary statistical tests for detecting nonlinearities in the deterministic part of SISO systems with noise. The most referenced method is unreliable for common noise processes as e.g.\\ colored. Therefore two new methods based on superposition and sinus input...

  16. Analytic solutions of a class of nonlinearly dynamic systems

    International Nuclear Information System (INIS)

    Wang, M-C; Zhao, X-S; Liu, X

    2008-01-01

    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

  17. Photon nonlinear mixing in subcarrier multiplexed quantum key distribution systems.

    Science.gov (United States)

    Capmany, José

    2009-04-13

    We provide, for the first time to our knowledge, an analysis of the influence of nonlinear photon mixing on the end to end quantum bit error rate (QBER) performance of subcarrier multiplexed quantum key distribution systems. The results show that negligible impact is to be expected for modulation indexes in the range of 2%.

  18. Turing instability in reaction-diffusion systems with nonlinear diffusion

    Energy Technology Data Exchange (ETDEWEB)

    Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

    2013-10-15

    The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

  19. Robust stabilization of nonlinear systems by quantized and ternary control

    NARCIS (Netherlands)

    Persis, Claudio De

    2009-01-01

    Results on the problem of stabilizing a nonlinear continuous-time minimum-phase system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by

  20. Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...

    Indian Academy of Sciences (India)

    chaos in four-dimensional space by the generalized definitions of spatial ... according to nonlinear noise in the real physical world, f(φ(x),ψ(x)) and g(φ(x) ... tion in ecological system, where φm,n(s) is the host density in generations s and s + 1,.

  1. Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation

    Directory of Open Access Journals (Sweden)

    A. Fereidoon

    2012-01-01

    Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.

  2. Explicit analytical solution of the nonlinear Vlasov Poisson system

    International Nuclear Information System (INIS)

    Skarka, V.; Mahajan, S.M.; Fijalkow, E.

    1993-10-01

    In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs

  3. Modelling and control of a nonlinear magnetostrictive actuator system

    Science.gov (United States)

    Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.

    2018-04-01

    This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.

  4. Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.

    2007-01-01

    Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves

  5. An introduction to complex systems society, ecology, and nonlinear dynamics

    CERN Document Server

    Fieguth, Paul

    2017-01-01

    This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or per...

  6. Nonlinear Dynamics, Chaotic and Complex Systems

    Science.gov (United States)

    Infeld, E.; Zelazny, R.; Galkowski, A.

    2011-04-01

    Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet

  7. On the power amplifier nonlinearity in MIMO transmit beamforming systems

    KAUST Repository

    Qi, Jian

    2012-03-01

    In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT. © 2012 IEEE.

  8. Upport vector machines for nonlinear kernel ARMA system identification.

    Science.gov (United States)

    Martínez-Ramón, Manel; Rojo-Alvarez, José Luis; Camps-Valls, Gustavo; Muñioz-Marí, Jordi; Navia-Vázquez, Angel; Soria-Olivas, Emilio; Figueiras-Vidal, Aníbal R

    2006-11-01

    Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA2K) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based system identification nonlinear models is presented, based on the use of composite Mercer's kernels. This general class can improve model flexibility by emphasizing the input-output cross information (SVM-ARMA4K), which leads to straightforward and natural combinations of implicit and explicit ARMA models (SVR-ARMA2K and SVR-ARMA4K). Capabilities of these different SVM-based system identification schemes are illustrated with two benchmark problems.

  9. On the power amplifier nonlinearity in MIMO transmit beamforming systems

    KAUST Repository

    Qi, Jian; Aissa, Sonia

    2012-01-01

    In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT. © 2012 IEEE.

  10. Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

    Science.gov (United States)

    Deng, Mao-Lin; Zhu, Wei-Qiu

    2016-08-01

    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

  11. Response of MDOF strongly nonlinear systems to fractional Gaussian noises

    International Nuclear Information System (INIS)

    Deng, Mao-Lin; Zhu, Wei-Qiu

    2016-01-01

    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

  12. Response of MDOF strongly nonlinear systems to fractional Gaussian noises

    Energy Technology Data Exchange (ETDEWEB)

    Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)

    2016-08-15

    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

  13. Evolution of the radiation protection system; L'evolution du systeme de protection radiologique

    Energy Technology Data Exchange (ETDEWEB)

    Clarke, R.H. [International Commission on Radiological Protection, Stockholm (Sweden); Schieber, C.; Cordoliani, Y.S. [Societe Francaise de Radioprotection, 92 - Fontenay aux Roses (France); Brechignac, F. [CEA Cadarache, Institut de Radioprotection et de Surete Nucleaire, Dept. de Protection de l' Environnement, 13 - Saint Paul Lez Durance (France)

    2003-07-01

    The evolution of the system of radiological protection: justification for new ICRP recommendations, thoughts of the SFRP work group about the evolution of the system of radiation protection proposed by the ICRP, protection of environment against ionizing radiations seen by the ICRP are the three parts of this chapter. (N.C.)

  14. Coupled diffusion systems with localized nonlinear reactions

    DEFF Research Database (Denmark)

    Pedersen, M.; Lin, Zhigui

    2001-01-01

    This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit - δui = ui+1Pi(x0, t), (i = 1,...,k, uk+1 := uu) in Ω × (0, T) with boundary conditions ui = 0 on ∂Ω × [0, T). We show that the solution has a global blowup. The exact rate...

  15. Nonlinear integrodifferential equations as discrete systems

    Science.gov (United States)

    Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

    1999-06-01

    We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

  16. Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

    Science.gov (United States)

    Herzallah, Randa

    2013-06-01

    Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.

  17. PWL approximation of nonlinear dynamical systems, part II: identification issues

    International Nuclear Information System (INIS)

    De Feo, O; Storace, M

    2005-01-01

    This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes a black-box identification method based on state space reconstruction and PWL approximation, and applies it to some particularly significant dynamical systems (two topological normal forms and the Colpitts oscillator)

  18. Global Linear Representations of Nonlinear Systems and the Adjoint Map

    OpenAIRE

    Banks, S.P.

    1988-01-01

    In this paper we shall study the global linearization of nonlinear systems on a manifold by two methods. The first consists of an expansion of the vector field in the space of square integrable vector fields. In the second method we use the adjoint representation of the Lie algebra vector fields to obtain an infinite-dimensional matrix representation of the system. A connection between the two approaches will be developed.

  19. Nonlinear degenerate cross-diffusion systems with nonlocal interaction

    OpenAIRE

    Di Francesco, M.; Esposito, A.; Fagioli, S.

    2017-01-01

    We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove g...

  20. The ATLAS Production System Evolution

    CERN Document Server

    Borodin, Mikhail; The ATLAS collaboration

    2017-01-01

    The second generation of the ATLAS Production System called ProdSys2 is a distributed workload manager that runs daily hundreds of thousands of jobs, from dozens of different ATLAS-specific workflows, across more than a hundred heterogeneous sites. It achieves high utilization by combining dynamic job definition based upon many criteria, such as input and output size, memory requirements and CPU consumption, with manageable scheduling policies and by supporting different kinds of computational resources, such as GRID, clouds, supercomputers and volunteer computers. The system dynamically assigns a group of jobs (task) to a group of geographically distributed computing resources. Dynamic assignment and resource utilization is one of the major features of the system. The Production System has a sophisticated job fault recovery mechanism, which efficiently allows running multi-terabyte tasks without human intervention. We have implemented new features which allow automatic task submission and chaining of differe...

  1. Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper

    Directory of Open Access Journals (Sweden)

    Hailong Zhang

    2015-01-01

    Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.

  2. Nonlinear quenches of power-law confining traps in quantum critical systems

    International Nuclear Information System (INIS)

    Collura, Mario; Karevski, Dragi

    2011-01-01

    We describe the coherent quantum evolution of a quantum many-body system with a time-dependent power-law confining potential. The amplitude of the inhomogeneous potential is driven in time along a nonlinear ramp which crosses a critical point. Using Kibble-Zurek-like scaling arguments we derive general scaling laws for the density of excitations and energy excess generated during the nonlinear sweep of the confining potential. It is shown that, with respect to the sweeping rate, the densities follow algebraic laws with exponents that depend on the space-time properties of the potential and on the scaling dimensions of the densities. We support our scaling predictions with both analytical and numerical results on the Ising quantum chain with an inhomogeneous transverse field varying in time.

  3. Novel procedure for characterizing nonlinear systems with memory: 2017 update

    Science.gov (United States)

    Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

    2017-05-01

    The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.

  4. Nonlinear damping based semi-active building isolation system

    Science.gov (United States)

    Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

    2018-06-01

    Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

  5. Geostrophic tripolar vortices in a two-layer fluid: Linear stability and nonlinear evolution of equilibria

    Science.gov (United States)

    Reinaud, J. N.; Sokolovskiy, M. A.; Carton, X.

    2017-03-01

    We investigate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate the nonlinear evolution of a few selected cases of tripoles.

  6. Non-linear macro evolution of a dc driven micro atmospheric glow discharge

    Energy Technology Data Exchange (ETDEWEB)

    Xu, S. F.; Zhong, X. X., E-mail: xxzhong@sjtu.edu.cn [The State Key Laboratory on Fiber Optic Local Area, Communication Networks and Advanced Optical Communication Systems, Key Laboratory for Laser Plasmas and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China)

    2015-10-15

    We studied the macro evolution of the micro atmospheric glow discharge generated between a micro argon jet into ambient air and static water. The micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors are found for the micro discharge when the water acts as a cathode, different from the discharge when water behaves as an anode. Groups of snapshots of the micro discharge formed at different discharge currents are captured by an intensified charge-coupled device with controlled exposure time, and each group consisted of 256 images taken in succession. Edge detection methods are used to identify the water surface and then the total brightness is defined by adding up the signal counts over the area of the micro discharge. Motions of the water surface at different discharge currents show that the water surface lowers increasingly rapidly when the water acts as a cathode. In contrast, the water surface lowers at a constant speed when the water behaves as an anode. The light curves are similar to logistic growth curves, suggesting that a self-inhibition process occurs in the micro discharge. Meanwhile, the total brightness increases linearly during the same time when the water acts as an anode. Discharge-water interactions cause the micro discharge to evolve. The charged particle bomb process is probably responsible for the different behaviors of the micro discharges when the water acts as cathode and anode.

  7. Scenarios for the nonlinear evolution of alpha particle induced Alfven wave instability

    International Nuclear Information System (INIS)

    Berk, H.L.; Breizman, B.N.; Ye, Huanchun.

    1992-03-01

    Various nonlinear scenarios are given for the evolution of energetic particles that are slowing down in a background plasma and simultaneously causing instability of the background plasma waves. If the background damping is sufficiently weak, a steady-state wave is established as described by Berk and Breizman. For larger background damping rate pulsations develop. Saturation occurs when the wave amplitude rises to where the wave trapping frequency equals the growth rate. The wave then damps due to the small background dissipation present and a relatively long quiet interval exists between bursts while the free energy of the distribution is refilled by classical transport. In this scenario the anomalous energy loss of energetic particles due to diffusion is small compared to the classical collisional energy exchange with the background plasma. However, if at the trapping frequency, the wave amplitude is large enough to cause orbit stochasticity, a phase space ''explosion'' occurs where the wave amplitudes rise to higher levels which leads to rapid loss of energetic particles

  8. Nonlinear evolution-type equations and their exact solutions using inverse variational methods

    International Nuclear Information System (INIS)

    Kara, A H; Khalique, C M

    2005-01-01

    We present the role of invariants in obtaining exact solutions of differential equations. Firstly, conserved vectors of a partial differential equation (p.d.e.) allow us to obtain reduced forms of the p.d.e. for which some of the Lie point symmetries (in vector field form) are easily concluded and, therefore, provide a mechanism for further reduction. Secondly, invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. In this latter case, the reductions carry all the usual advantages regarding Noether symmetries and double reductions. The examples we consider are nonlinear evolution-type equations such as the Korteweg-deVries equation, but a detailed analysis is made on the Fisher equation (which describes reaction-diffusion waves in biology, inter alia). Other diffusion-type equations lend themselves well to the method we describe (e.g., the Fitzhugh Nagumo equation, which is briefly discussed). Some aspects of Painleve properties are also suggested

  9. Influence of helical external driven current on nonlinear resistive tearing mode evolution and saturation in tokamaks

    Science.gov (United States)

    Zhang, W.; Wang, S.; Ma, Z. W.

    2017-06-01

    The influences of helical driven currents on nonlinear resistive tearing mode evolution and saturation are studied by using a three-dimensional toroidal resistive magnetohydrodynamic code (CLT). We carried out three types of helical driven currents: stationary, time-dependent amplitude, and thickness. It is found that the helical driven current is much more efficient than the Gaussian driven current used in our previous study [S. Wang et al., Phys. Plasmas 23(5), 052503 (2016)]. The stationary helical driven current cannot persistently control tearing mode instabilities. For the time-dependent helical driven current with f c d = 0.01 and δ c d < 0.04 , the island size can be reduced to its saturated level that is about one third of the initial island size. However, if the total driven current increases to about 7% of the total plasma current, tearing mode instabilities will rebound again due to the excitation of the triple tearing mode. For the helical driven current with time dependent strength and thickness, the reduction speed of the radial perturbation component of the magnetic field increases with an increase in the driven current and then saturates at a quite low level. The tearing mode is always controlled even for a large driven current.

  10. Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

    Directory of Open Access Journals (Sweden)

    V. O. Vakhnenko

    2016-01-01

    Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

  11. Study of a nonlinear system with shocks under broadband excitation. Application to a steam generator tube

    International Nuclear Information System (INIS)

    Thenint, Th.

    2011-01-01

    The steam generator is a heat exchanger and participates to the nuclear safety. Energy is transferred from the primary to the secondary fluid through many U-tubes maintained vertically by support plates. A sludge deposit tends to modify the boundary conditions and the secondary fluid flow. A fluid-elastic instability can then occur and lead to quick tube ruin. This thesis seeks a better understanding of the effect of contact nonlinearity on the dynamics of a tube in-air intermittently impacting the support plates and its consequences in regards with instability. The use of discretized contact conditions with circular obstacles distributed over the thickness of the plates and the use of enriched reduction bases allow quick and relevant nonlinear numerical simulations. These simulations are well correlated with experimental measurements and valid even with strong nonlinearity or negative modal damping. The evolution of power spectral densities (PSD) with growing excitation amplitude is analyzed: padding of the anti-resonances, peak shift and spread. It is then shown that an apparent stiffness associated with a permanent bilateral contact is pertinent to describe these transitions. In the case of an unstable linear system, one demonstrates that the nonlinearity keeps the responses bounded or stabilised, thus paving the way for future work with real or simulated fluid flows. (author)

  12. Evolution of Linux operating system network

    Science.gov (United States)

    Xiao, Guanping; Zheng, Zheng; Wang, Haoqin

    2017-01-01

    Linux operating system (LOS) is a sophisticated man-made system and one of the most ubiquitous operating systems. However, there is little research on the structure and functionality evolution of LOS from the prospective of networks. In this paper, we investigate the evolution of the LOS network. 62 major releases of LOS ranging from versions 1.0 to 4.1 are modeled as directed networks in which functions are denoted by nodes and function calls are denoted by edges. It is found that the size of the LOS network grows almost linearly, while clustering coefficient monotonically decays. The degree distributions are almost the same: the out-degree follows an exponential distribution while both in-degree and undirected degree follow power-law distributions. We further explore the functionality evolution of the LOS network. It is observed that the evolution of functional modules is shown as a sequence of seven events (changes) succeeding each other, including continuing, growth, contraction, birth, splitting, death and merging events. By means of a statistical analysis of these events in the top 4 largest components (i.e., arch, drivers, fs and net), it is shown that continuing, growth and contraction events occupy more than 95% events. Our work exemplifies a better understanding and describing of the dynamics of LOS evolution.

  13. The role of collective self-gravity in the nonlinear evolution of viscous overstability in Saturn's rings.

    Science.gov (United States)

    Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

    2017-06-01

    We investigate the influence of collective self-gravity forces on the nonlinear evolution of the viscous overstability in Saturn's dense rings. Local N-body simulations, incorporating vertical and radial collective self-gravity are performed. Vertical self-gravity is mimicked through an increased frequency of vertical oscillations, while radial self-gravity is approximated by solving the Poisson equation for a thin disk in Fourier space. Direct particle-particle forces are omitted, while the magnitude of radial self gravity is controlled by assigning a variable surface mass density to the system's homogeneous ground state. We compare our simulations with large-scale isothermal and non-isothermal hydrodynamic model calculations, including radial self-gravity and employing transport coefficients derived in Salo et al. (2001). We concentrate on optical depths τ=1.5-2, appropriate to model Saturn's dense rings. Our isothermal and non isothermal hydrodynamic results in the limit of vanishing self-gravity compare very well with the studies of Latter&Ogilvie (2010) and Rein&latter (2013), respectively.With non-vanishing radial self-gravity we find that the wavelengths of saturated overstable wave trains are located in close vicinity of the local minimum of the nonlinear dispersion relation for a particular surface density. Good agreement is found between non-isothermal hydrodynamics and N-body simulations for disks with strong radial self-gravity, while the largest deviations occur for a weak but non-vanishing self-gravity.The resulting saturation wavelengths of the viscous overstability for moderate and strong radial self-gravity (λ~ 200-300m) agree reasonably well with the length scale of periodic micro structure in Saturn's inner A and B ring, as found by Cassini.

  14. The non-linear evolution of magnetic flux ropes: 3. effects of dissipation

    Directory of Open Access Journals (Sweden)

    C. J. Farrugia

    1997-02-01

    Full Text Available We study the evolution (expansion or oscillation of cylindrically symmetric magnetic flux ropes when the energy dissipation is due to a drag force proportional to the product of the plasma density and the radial speed of expansion. The problem is reduced to a single, second-order, ordinary differential equation for a damped, non-linear oscillator. Motivated by recent work on the interplanetary medium and the solar corona, we consider polytropes whose index, γ, may be less than unity. Numerical analysis shows that, in contrast to the small-amplitude case, large-amplitude oscillations are quasi-periodic with frequencies substantially higher than those of undamped oscillators. The asymptotic behaviour described by the momentum equation is determined by a balance between the drag force and the gradient of the gas pressure, leading to a velocity of expansion of the flux rope which may be expressed as (1/2γr/t, where r is the radial coordinate and t is the time. In the absence of a drag force, we found in earlier work that the evolution depends both on the polytropic index and on a dimensionless parameter, κ. Parameter κ was found to have a critical value above which oscillations are impossible, and below which they can exist only for energies less than a certain energy threshold. In the presence of a drag force, the concept of a critical κ remains valid, and when κ is above critical, the oscillatory mode disappears altogether. Furthermore, critical κ remains dependent only on γ and is, in particular, independent of the normalized drag coefficient, ν*. Below critical κ, however, the energy required for the flux rope to escape to infinity depends not only on κ (as in the conservative force case but also on ν*. This work indicates how under certain conditions a small change in the viscous drag coefficient or the initial energy may alter the evolution drastically. It is thus important to determine ν* and κ from observations.

  15. On the asymptotic stability of nonlinear mechanical switched systems

    Science.gov (United States)

    Platonov, A. V.

    2018-05-01

    Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

  16. Reduced Complexity Volterra Models for Nonlinear System Identification

    Directory of Open Access Journals (Sweden)

    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.

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

    International Nuclear Information System (INIS)

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

    2013-01-01

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

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

    Science.gov (United States)

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

    2013-05-01

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

  19. New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs

    Science.gov (United States)

    Venturi, D.; Karniadakis, G. E.

    2012-08-01

    By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.

  20. The evolution time of nucleon spectrum in residual excited nucleus and calculation of the non-linear effects

    International Nuclear Information System (INIS)

    Kenzhebaev, Sh.K.; Djuraev, Sh.H.; Mannanov, D.E.; Khugaev, A.V.

    1994-01-01

    The investigation of nonstationary fermi-gas thermalization of nucleons in the residual excited nucleus as an open nonlinearize system and analytical methods of calculation are presented. (author). 9 refs

  1. Nonlinear noninteger order circuits and systems an introduction

    CERN Document Server

    Arena, P; Fortuna, L; Porto, D

    2001-01-01

    In this book, the reader will find a theoretical introduction to noninteger order systems, as well as several applications showing their features and peculiarities. The main definitions and results of research on noninteger order systems and modelling of physical noninteger phenomena are reported together with problems of their approximation. Control applications, noninteger order CNNs and circuit realizations of noninteger order systems are also presented.The book is intended for students and researchers involved in the simulation and control of nonlinear noninteger order systems, with partic

  2. Spatio-temporal modeling of nonlinear distributed parameter systems

    CERN Document Server

    Li, Han-Xiong

    2011-01-01

    The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein s

  3. On the orthogonalised reverse path method for nonlinear system identification

    Science.gov (United States)

    Muhamad, P.; Sims, N. D.; Worden, K.

    2012-09-01

    The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.

  4. Evolution of genetic systems in filamentous ascomycetes

    NARCIS (Netherlands)

    Nauta, M.J.

    1994-01-01

    A great variety of genetic systems exist in filamentous ascomycetes. The transmission of genetic material does not only occur by (sexual or asexual) reproduction, but it can also follow vegetative fusion of different strains. In this thesis the evolution of this variability is studied,

  5. Nonlinear dynamic analysis of nuclear reactor primary coolant systems

    International Nuclear Information System (INIS)

    Saffell, B.F. Jr.; Macek, R.W.; Thompson, T.R.; Lippert, R.F.

    1979-01-01

    The ADINA computer code is utilized to perform mechanical response analysis of pressurized reactor primary coolant systems subjected to postulated loss-of-coolant accident (LOCA) loadings. Specifically, three plant analyses are performed utilizing the geometric and material nonlinear analysis capabilities of ADINA. Each reactor system finite element model represents the reactor vessel and internals, piping, major components, and component supports in a single coupled model. Material and geometric nonlinear capabilities of the beam and truss elements are employed in the formulation of each finite element model. Loadings applied to each plant for LOCA dynamic analysis include steady-state pressure, dead weight, strain energy release, transient piping hydraulic forces, and reactor vessel cavity pressurization. Representative results are presented with some suggestions for consideration in future ADINA code development

  6. Nonlinear transport properties of non-ideal systems

    International Nuclear Information System (INIS)

    Pavlov, G A

    2009-01-01

    The theory of nonlinear transport is elaborated to determine the Burnett transport properties of non-ideal multi-element plasma and neutral systems. The procedure for the comparison of the phenomenological conservation equations of a continuous dense medium and the microscopic equations for dynamical variable operators is used for the definition of these properties. The Mori algorithm is developed to derive the equations of motion of dynamical value operators of a non-ideal system in the form of the generalized nonlinear Langevin equations. In consequence, the microscopic expressions of transport coefficients corresponding to second-order thermal disturbances (temperature, mass velocity, etc) have been found in the long wavelength and low frequency limits

  7. Information theory and stochastics for multiscale nonlinear systems

    CERN Document Server

    Majda, Andrew J; Grote, Marcus J

    2005-01-01

    This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...

  8. Extinction in Two-Species Nonlinear Discrete Competitive System

    Directory of Open Access Journals (Sweden)

    Liqiong Pu

    2016-01-01

    Full Text Available We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.

  9. On a mixed problem for a coupled nonlinear system

    Directory of Open Access Journals (Sweden)

    Marcondes R. Clark

    1997-03-01

    Full Text Available In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dxDelta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.

  10. Nonlinear Fourier transform for dual-polarization optical communication system

    OpenAIRE

    Gaiarin, Simone

    2018-01-01

    New services and applications are causing an exponential increase in the internet traffic. In a few years, the current fiber-optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically limits the information transmission rate. Eigenvalue communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering trans...

  11. THE EVOLUTION OF ACCOUNTING INFORMATION SYSTEMS

    Directory of Open Access Journals (Sweden)

    Andreea C. BENDOVSCHI

    2015-04-01

    Full Text Available Technological evolution becomes more and more a daily reality for businesses and individuals who use information systems as for supporting their operational activities. This article focuses on the way technological evolution changes the accounting practices, starting from the analysis of the traditional model and trying to determine future trends and arising challenges to face. From data input to consolidation and reporting, accountants’ function and operations are dissected in order to identify to what extent the development of new concepts, such as cloud computing, cloud accounting, real-time accounting or mobile accounting may affect the financial-accounting process, as well as the challenges that arise from the changing environment.

  12. Evolution of toxicology information systems

    Energy Technology Data Exchange (ETDEWEB)

    Wassom, J.S.; Lu, P.Y. [Oak Ridge National Laboratory, TN (United States)

    1990-12-31

    Society today is faced with new health risk situations that have been brought about by recent scientific and technical advances. Federal and state governments are required to assess the many potential health risks to exposed populations from the products (chemicals) and by-products (pollutants) of these advances. Because a sound analysis of any potential health risk should be based on the use of relevant information, it behooves those individuals responsible for making the risk assessments to know where to obtain needed information. This paper reviews the origins of toxicology information systems and explores the specialized information center concept that was proposed in 1963 as a means of providing ready access to scientific and technical information. As a means of illustrating this concept, the operation of one specialized information center (the Environmental Mutagen Information Center at Oak Ridge National Laboratory) will be discussed. Insights into how toxicological information resources came into being, their design and makeup, will be of value to those seeking to acquire information for risk assessment purposes. 7 refs., 1 fig., 4 tabs.

  13. Periodic and solitary wave solutions of cubic–quintic nonlinear ...

    Indian Academy of Sciences (India)

    Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.

  14. Data based identification and prediction of nonlinear and complex dynamical systems

    Science.gov (United States)

    Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

    2016-07-01

    The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical

  15. Data based identification and prediction of nonlinear and complex dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Wen-Xu [School of Systems Science, Beijing Normal University, Beijing, 100875 (China); Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Lai, Ying-Cheng, E-mail: Ying-Cheng.Lai@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Grebogi, Celso [Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom)

    2016-07-12

    The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear

  16. Data based identification and prediction of nonlinear and complex dynamical systems

    International Nuclear Information System (INIS)

    Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

    2016-01-01

    The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear

  17. Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

    International Nuclear Information System (INIS)

    Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E

    2012-01-01

    Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

  18. Synchronization in Complex Networks of Nonlinear Dynamical Systems

    CERN Document Server

    Wu, Chai Wah

    2007-01-01

    This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ide

  19. Chaotic dynamics and chaos control in nonlinear laser systems

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    2001-01-01

    Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally

  20. On the stability of non-linear systems

    International Nuclear Information System (INIS)

    Guelman, M.

    1968-09-01

    A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [fr

  1. Boundary control of nonlinear coupled heat systems using backstepping

    KAUST Repository

    Bendevis, Paul

    2016-10-20

    A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.

  2. Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty

    NARCIS (Netherlands)

    van der Schaft, Arjan

    1995-01-01

    The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust

  3. Nonlinear evolution in Quantum Chromodynamics and its application to neutrinos production at very high energy

    International Nuclear Information System (INIS)

    Stasto, A.

    2004-09-01

    This work is a study of the phenomenon of partonic saturation in the high energy collisions of elementary particles. We have observed the geometric scaling property of the deep inelastic electron-proton cross section which can be interpreted as a signal of partonic saturation. This scaling means that the cross section depends only on one scaling variable τ ≅ Q 2 /Q 2 s (x) which is a ratio of the photon virtuality Q 2 and the saturation scale Q 2 s (x) which depends power-like on Bjorken x. The properties of the solution to the linear DGLAP evolution equations have been investigated in the presence of the scaling initial conditions. These conditions are given on the critical line defined as Q 0 =Q 4 s (x). In the fixed strong coupling case scaling is preserved by the DGLAP evolution. When strong coupling is running, geometric scaling is violated because of presence of additional scale Λ QCD . The coefficient responsible for geometric scaling violations has been extracted, which vanishes for very small values of Bjorken x such that Q 2 4 s (x)=Λ 2 QCD . We have analysed numerically nonlinear Balitsky-Kovchegov equation, which takes into account diagrams responsible for the gluon recombination and describes partonic saturation. The solution to this equation in the case of the infinitely large target has been obtained (1 + 1 dimensions). In the linear case, the solution is plagued by the strong diffusion of the transverse momenta. It turns out that in the nonlinear equation the diffusion to infrared region is strongly suppressed due to the presence of the saturation scale Q s (x). We have also investigated the impact of the nonleading in x effects in this equation such as running coupling and the consistency constraint. In the case of solution to the Balitsky-Kovchegov equation in 3+1 dimensions the power behaviour in impact parameter is present, even if the initial conditions are exponentially falling. This feature causes violation of the Froissart-Martin bound

  4. Computer Simulation of Hydraulic Systems with Typical Nonlinear Characteristics

    Directory of Open Access Journals (Sweden)

    D. N. Popov

    2017-01-01

    Full Text Available The task was to synthesise an adjustable hydraulic system structure, the mathematical model of which takes into account its inherent nonlinearity. Its solution suggests using a successive computer simulations starting with a structure of the linearized stable hydraulic system, which is then complicated by including the essentially non-linear elements. The hydraulic system thus obtained may be unable to meet the Lyapunov stability criterion and be unstable. This can be eliminated through correcting elements. Control of correction results is provided according to the form of transition processes due to stepwise variation of the control signal.Computer simulation of a throttle-controlled electrohydraulic servo drive with the rotary output element illustrates the proposed method application. A constant pressure power source provides fluid feed for the drive under pressure.For drive simulation the following models were involved: the linear model, the model taking into consideration a non-linearity of the flow-dynamic characteristics of a spool-type valve, and the non-linear models that take into account the dry friction in the spool-type valve, the backlash in the steering angle sensor of the motor shaft.The paper shows possibility of damping oscillation caused by variable hydrodynamic forces through introducing a correction device.The list of references attached contains 16 sources, which were used to justify and explain certain factors of the automatic control theory and the fluid mechanics of unsteady flows.The article presents 6 block-diagrams of the electrohydraulic servo drive and their appropriate transition processes, which have been studied.

  5. Global chaos synchronization of new chaotic systems via nonlinear control

    International Nuclear Information System (INIS)

    Chen, H.-K.

    2005-01-01

    Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach

  6. Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

    CERN Document Server

    Petráš, Ivo

    2011-01-01

    "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

  7. Nonlinear dynamical systems for theory and research in ergonomics.

    Science.gov (United States)

    Guastello, Stephen J

    2017-02-01

    Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

  8. Neural networks for feedback feedforward nonlinear control systems.

    Science.gov (United States)

    Parisini, T; Zoppoli, R

    1994-01-01

    This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

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

    Science.gov (United States)

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

    2009-12-01

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

  10. Quantum dynamical effects as a singular perturbation for observables in open quasi-classical nonlinear mesoscopic systems

    International Nuclear Information System (INIS)

    Berman, G.P.; Borgonovi, F.; Dalvit, D.A.R.

    2009-01-01

    We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a singular 'quantum' perturbation for observables in some 'mesoscopic' region of parameters. In particular, quantum effects result in secular terms in the dynamical evolution, that grow in time. We argue that even for open quantum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after decoherence and relaxation processes take place. We demonstrate that these quantum effects in open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states. In particular, we show that for Bose-Einstein condensate systems the characteristic time of deviation of quantum dynamics for observables from the corresponding classical dynamics coincides with the characteristic time-scale of the well-known quantum nonlinear effect of phase diffusion.

  11. System Reduction in Nonlinear Multibody Dynamics of Wind Turbines

    DEFF Research Database (Denmark)

    Holm-Jørgensen, Kristian; Nielsen, Søren R.K.; Rubak, Rune

    2007-01-01

    In this paper the system reduction in nonlinear multibody dynamics of wind turbines is investigated for various updating schemes of the moving frame of reference. In one case, the moving frame of reference is updated to a stiff body, relative to which the elastic deformations are fixed at one end....... In the other case, the stiff body motion is defined as the chord line connecting the end points of the beam, and the elastic deformations are simply supported at the end points. The system reduction is performed by discretizing the spatial motion into a set of rigid body modes and linear elastic eigenmodes...

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

    Directory of Open Access Journals (Sweden)

    I. Estrada-Sánchez

    2017-01-01

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

  13. Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient

    Directory of Open Access Journals (Sweden)

    Zaiyue Yang

    2014-01-01

    Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.

  14. Nonlinear dynamics of global atmospheric and earth system processes

    Science.gov (United States)

    Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu

    1995-01-01

    During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.

  15. Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

    Directory of Open Access Journals (Sweden)

    Qingkai Han

    2014-01-01

    Full Text Available The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.

  16. Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

    CERN Document Server

    Aliyu, MDS

    2011-01-01

    A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

  17. Observer-based Fault Detection and Isolation for Nonlinear Systems

    DEFF Research Database (Denmark)

    Lootsma, T.F.

    With the rise in automation the increase in fault detectionand isolation & reconfiguration is inevitable. Interest in fault detection and isolation (FDI) for nonlinear systems has grown significantly in recent years. The design of FDI is motivated by the need for knowledge about occurring faults...... in fault-tolerant control systems (FTC systems). The idea of FTC systems is to detect, isolate, and handle faults in such a way that the systems can still perform in a required manner. One prefers reduced performance after occurrence of a fault to the shut down of (sub-) systems. Hence, the idea of fault......-output decoupling is described. It is a new idea based on the solution of the input-output decoupling problem. The idea is to include FDI considerations already during the control design....

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

    International Nuclear Information System (INIS)

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

    2015-01-01

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

  19. Develop advanced nonlinear signal analysis topographical mapping system

    Science.gov (United States)

    1994-01-01

    The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of

  20. Analyzing systemic risk using non-linear marginal expected shortfall and its minimum spanning tree

    Science.gov (United States)

    Song, Jae Wook; Ko, Bonggyun; Chang, Woojin

    2018-02-01

    The aim of this paper is to propose a new theoretical framework for analyzing the systemic risk using the marginal expected shortfall (MES) and its correlation-based minimum spanning tree (MST). At first, we develop two parametric models of MES with their closed-form solutions based on the Capital Asset Pricing Model. Our models are derived from the non-symmetric quadratic form, which allows them to consolidate the non-linear relationship between the stock and market returns. Secondly, we discover the evidences related to the utility of our models and the possible association in between the non-linear relationship and the emergence of severe systemic risk by considering the US financial system as a benchmark. In this context, the evolution of MES also can be regarded as a reasonable proxy of systemic risk. Lastly, we analyze the structural properties of the systemic risk using the MST based on the computed series of MES. The topology of MST conveys the presence of sectoral clustering and strong co-movements of systemic risk leaded by few hubs during the crisis. Specifically, we discover that the Depositories are the majority sector leading the connections during the Non-Crisis period, whereas the Broker-Dealers are majority during the Crisis period.

  1. Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

    Science.gov (United States)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

    We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

  2. A generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system

    NARCIS (Netherlands)

    Yang, Y.; Solis Escalante, T.; van der Helm, F.C.T.; Schouten, A.C.

    2016-01-01

    Objective: This paper introduces a generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system, namely cross-spectral coherence (CSC). CSC can detect different types of nonlinear interactions including harmonic and intermodulation coupling as present

  3. Tidal instability in exoplanetary systems evolution

    Directory of Open Access Journals (Sweden)

    Le Gal P.

    2011-02-01

    Full Text Available A new element is proposed to play a role in the evolution of extrasolar planetary systems: the tidal (or elliptical instability. It comes from a parametric resonance and takes place in any rotating fluid whose streamlines are (even slightly elliptically deformed. Based on theoretical, experimental and numerical works, we estimate the growth rate of the instability for hot-jupiter systems, when the rotation period of the star is known. We present the physical process, its application to stars, and preliminary results obtained on a few dozen systems, summarized in the form of a stability diagram. Most of the systems are trapped in the so-called "forbidden zone", where the instability cannot grow. In some systems, the tidal instability is able to grow, at short timescales compared to the system evolution. Implications are discussed in the framework of misaligned transiting systems, as the rotational axis of the star would be unstable in systems where this elliptical instability grows.

  4. Linear and nonlinear dynamic systems in financial time series prediction

    Directory of Open Access Journals (Sweden)

    Salim Lahmiri

    2012-10-01

    Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.

  5. Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

    Science.gov (United States)

    Raju, Thokala Soloman; Pal, Ritu

    2018-05-01

    We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

  6. Nonlinear wave-beam kinetic equilibrium in decelerating systems

    International Nuclear Information System (INIS)

    Grishin, V.K.; Shaposhnikova, E.N.

    1981-01-01

    The equilibrium state of the wave-beam system arising during the interaction of a particle beam and excited electromagnetic wave has been investigated on the basis of the analysis of the exact polution of a non-linear self-consistent linear equation using the complete system of conservation laws. A waveguide with a dielectric filler, into which a monoenergetic particle beam magnetized in a transverse plane is continuously injected, is used as a model of an decelerating system. A dispersion equation describing the system state and expression for the evaluation of efficiency of the beam energy conversion to the field energy have been obtained. It is concluded that larae fields and high efficiency of energy conversion are achieved during the marked beam reconstruction. States with different values of current and beam velocity but similar amplitudes of a longitudinal field are possible in the system considered [ru

  7. Linear theory for filtering nonlinear multiscale systems with model error.

    Science.gov (United States)

    Berry, Tyrus; Harlim, John

    2014-07-08

    In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering

  8. Evolution of tsunami warning systems and products.

    Science.gov (United States)

    Bernard, Eddie; Titov, Vasily

    2015-10-28

    Each year, about 60 000 people and $4 billion (US$) in assets are exposed to the global tsunami hazard. Accurate and reliable tsunami warning systems have been shown to provide a significant defence for this flooding hazard. However, the evolution of warning systems has been influenced by two processes: deadly tsunamis and available technology. In this paper, we explore the evolution of science and technology used in tsunami warning systems, the evolution of their products using warning technologies, and offer suggestions for a new generation of warning products, aimed at the flooding nature of the hazard, to reduce future tsunami impacts on society. We conclude that coastal communities would be well served by receiving three standardized, accurate, real-time tsunami warning products, namely (i) tsunami energy estimate, (ii) flooding maps and (iii) tsunami-induced harbour current maps to minimize the impact of tsunamis. Such information would arm communities with vital flooding guidance for evacuations and port operations. The advantage of global standardized flooding products delivered in a common format is efficiency and accuracy, which leads to effectiveness in promoting tsunami resilience at the community level. © 2015 The Authors.

  9. Evolution of tsunami warning systems and products

    Science.gov (United States)

    Bernard, Eddie; Titov, Vasily

    2015-01-01

    Each year, about 60 000 people and $4 billion (US$) in assets are exposed to the global tsunami hazard. Accurate and reliable tsunami warning systems have been shown to provide a significant defence for this flooding hazard. However, the evolution of warning systems has been influenced by two processes: deadly tsunamis and available technology. In this paper, we explore the evolution of science and technology used in tsunami warning systems, the evolution of their products using warning technologies, and offer suggestions for a new generation of warning products, aimed at the flooding nature of the hazard, to reduce future tsunami impacts on society. We conclude that coastal communities would be well served by receiving three standardized, accurate, real-time tsunami warning products, namely (i) tsunami energy estimate, (ii) flooding maps and (iii) tsunami-induced harbour current maps to minimize the impact of tsunamis. Such information would arm communities with vital flooding guidance for evacuations and port operations. The advantage of global standardized flooding products delivered in a common format is efficiency and accuracy, which leads to effectiveness in promoting tsunami resilience at the community level. PMID:26392620

  10. World-System and Evolution: An Appraisal

    Directory of Open Access Journals (Sweden)

    Thomas D. Hall

    2015-08-01

    Full Text Available This paper makes six arguments. First, socio-cultural evolution must be studied from a "world-system" or intersocietal interaction perspective. A focus on change in individual "societies" or "groups" fails to attend adequately to the effects of intersocietal interaction on social and cultural change. Second, in order to be useful, theories of the modern world-system must be modified extensively to deal with non-capitalist settings. In particular, changes in system boundaries marked by exchange networks (for information, luxury or prestige goods, political/military interactions, and bulk goods seldom coincide,and follow different patterns of change. Third, all such systems tend to pulsate, that is, expand and contract, or at least expand rapidly and less rapidly. Fourth, once hierarchical forms of social organization develop such systems typically have cycles of rise and fall in the relative positions of constituent politics. Fifth, expansion of world-systems forms and transforms social relations in newly incorporated areas. While complex in the modern world-system, these changes are even more complex in precapitalist settings. Sixth, thesetwo cycles combine with demographic and epidemiological processes to shape long -term socio-cultural evolution.

  11. Investigation of the Nonlinear Model of the Cellular Population System Development

    Directory of Open Access Journals (Sweden)

    M. S. Vinogradova

    2014-01-01

    Full Text Available An isolated population system is considered which consists of two types of human stem cells: normal cells and cells with chromosomal anomalies (abnormal. In the paper the nonlinear dynamic model which describes dynamics of cell populations developing in vitro is elaborated. The model allows to investigate the processes of the formation of the abnormal cells population from the abnormal cells population of normal cells as well as joint development of these populations. The model takes into account the limited resources.An important feature of the developed model is the use of biological characteristics of processes in the cell population system, such as the proportion of cells, divided over a specified time, the proportion of cells whish are not divided, and which are "lost" and which are passed in the population of abnormal cells from the normal population. This approach allows a more detailed analysis of the impact of various "primary" parameters on the evolution of the population system.Under cultivation of cell populations in vitro a struggle for resources primarily affects the processes of the cell reproduction. This is reflected in the existence of the dividing cells frequency dependence of the total population of normal and abnormal cells. For the account of such dependencies different non-linear functions are typically used. However, the use of such non-linear relationships leads to the difficulties in finding confidence intervals for the estimates of the model parameters at subsequent stages of research. At the same time, the problem of the system parameters estimating and finding of the corresponding confidence intervals for estimates can be solved easy in case when the nonlinear system is linear with respect to the unknown parameters. In the paper it is achieved due to the piecewise linear approximation of nonlinear dependencies.An important feature of the model is a different view of the right part of the differential equations system

  12. Fully nonlinear phenomenology of the Berk-Breizman augmentation of the Vlasov-Maxwell system

    International Nuclear Information System (INIS)

    Vann, R.G.L.; Dendy, R.O.; Rowlands, G.; Arber, T.D.; D'Ambrumenil, N.

    2003-01-01

    The Berk-Breizman augmentation of the Vlasov-Maxwell system is widely used to model self-consistent resonant excitation and damping of wave fields by evolving energetic particle populations in magnetic fusion plasmas. The key model parameters are the particle annihilation rate ν a , which drives bump-on-tail structure, and the linear wave damping rate γ d . A code, based on the piecewise parabolic method, is used to integrate the fully nonlinear Berk-Breizman system of equations across the whole (ν a ,γ d ) parameter space. The results of this code show that the system's behavior can be classified into one of four types, each of which occurs in a well-defined region of parameter space: chaotic, periodic, steady state, and damped. The corresponding evolution in (x,v) phase space is also examined

  13. Parameter and state estimation in nonlinear dynamical systems

    Science.gov (United States)

    Creveling, Daniel R.

    This thesis is concerned with the problem of state and parameter estimation in nonlinear systems. The need to evaluate unknown parameters in models of nonlinear physical, biophysical and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. When verifying and validating these models, it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, this thesis develops a framework for presenting data to a candidate model of a physical process in a way that makes efficient use of the measured data while allowing for estimation of the unknown parameters in the model. The approach presented here builds on existing work that uses synchronization as a tool for parameter estimation. Some critical issues of stability in that work are addressed and a practical framework is developed for overcoming these difficulties. The central issue is the choice of coupling strength between the model and data. If the coupling is too strong, the model will reproduce the measured data regardless of the adequacy of the model or correctness of the parameters. If the coupling is too weak, nonlinearities in the dynamics could lead to complex dynamics rendering any cost function comparing the model to the data inadequate for the determination of model parameters. Two methods are introduced which seek to balance the need for coupling with the desire to allow the model to evolve in its natural manner without coupling. One method, 'balanced' synchronization, adds to the synchronization cost function a requirement that the conditional Lyapunov exponents of the model system, conditioned on being driven by the data, remain negative but small in magnitude. Another method allows the coupling between the data and the model to vary in time according to a specific form of differential equation. The coupling dynamics is damped to allow for a tendency toward zero coupling

  14. Lotka-Volterra representation of general nonlinear systems.

    Science.gov (United States)

    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.

  15. On Madelung systems in nonlinear optics: A reciprocal invariance

    Science.gov (United States)

    Rogers, Colin; Malomed, Boris

    2018-05-01

    The role of the de Broglie-Bohm potential, originally established as central to Bohmian quantum mechanics, is examined for two canonical Madelung systems in nonlinear optics. In a seminal case, a Madelung system derived by Wagner et al. via the paraxial approximation and in which the de Broglie-Bohm potential is present is shown to admit a multi-parameter class of what are here introduced as "q-gaussons." In the limit, as the Tsallis parameter q → 1, the q-gaussons are shown to lead to standard gausson solitons, as admitted by the logarithmic nonlinear Schrödinger equation encapsulating the Madelung system. The q-gaussons are obtained for optical media with dual power-law refractive index. In the second case, a Madelung system originally derived via an eikonal approximation in the context of laser beam propagation and in which the de Broglie Bohm term is neglected is shown to admit invariance under a novel class of two-parameter class of reciprocal transformations. Model optical laws analogous to the celebrated Kármán-Tsien law of classical gas dynamics are introduced.

  16. Nonlinear Time-Reversal in a Wave Chaotic System

    Science.gov (United States)

    Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven

    2012-02-01

    Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)

  17. The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

    2007-05-01

    The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

  18. Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

    Science.gov (United States)

    Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

    2018-04-01

    Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

  19. Optimal the tilt angles for photovoltaic modules using PSO method with nonlinear time-varying evolution

    International Nuclear Information System (INIS)

    Chang, Ying-Pin

    2010-01-01

    A particle-swarm optimization method with nonlinear time-varying evolution (PSO-NTVE) is employed in determining the tilt angle of photovoltaic (PV) modules in Taiwan. The objective is to maximize the output electrical energy of the modules. In this study, seven Taiwanese cities were selected for analysis. First, the sun's position at any time and location was predicted by the mathematical procedure of Julian dating, and then the solar irradiation was obtained at each site under a clear sky. By combining the temperature effect, the PSO-NTVE method is adopted to calculate the optimal tilt angles for fixed south-facing PV modules. In this method, the parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments have an effect that approximates the full factorial experiments. Statistical error analysis was performed to compare the results between the four PSO methods and experimental results. Hengchun city in which the minimum total error value of 6.12% the reasons for the weather more stability and less building shade. A comparison of the measurement results in electrical energy between the four PSO methods and the PV modules set a six tilt angles. Obviously four types of PSO methods simulation of electrical energy value from 231.12 kWh/m 2 for Taipei to 233.81 kWh/m 2 for Hengchun greater than the measurement values from 224.71 kWh/m 2 for Taichung to 228.47 kWh/m 2 for Hengchun by PV module which is due to instability caused by climate change. Finally, the results show that the annual optimal angle for the Taipei area is 18.16 o ; for Taichung, 17.3 o ; for Tainan, 16.15 o ; for Kaosiung, 15.79 o ; for Hengchung, 15.17 o ; for Hualian, 17.16 o ; and for Taitung, 15.94 o . It is evident that the authorized Industrial Technology Research Institute (ITRI) recommends that tilt angle of 23.5 o was not an appropriate use of Taiwan's seven cities. PV modules with the installation of the tilt angle should be

  20. Jump phenomena. [large amplitude responses of nonlinear systems

    Science.gov (United States)

    Reiss, E. L.

    1980-01-01

    The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

  1. Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Junhai Luo

    2014-01-01

    Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.

  2. A universal approach to the study of nonlinear systems

    Science.gov (United States)

    Hwa, Rudolph C.

    2004-07-01

    A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.

  3. Foundations of Complex Systems Nonlinear Dynamics, Statistical Physics, and Prediction

    CERN Document Server

    Nicolis, Gregoire

    2007-01-01

    Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, h

  4. Nonlinear behaviors of a bounded electron beam-plasma system

    International Nuclear Information System (INIS)

    Iizuka, Satoru; Saeki, Koichi; Sato, Noriyoshi; Hatta, Yoshisuke

    1985-01-01

    Nonlinear developments of a bounded electron beam-plasma system including stationary electrons are investigated experimentally. A stable double layer is formed as a result of ion trapping in a growing negative potential dip induced by the Pierce instability above the current regime of the Buneman instability. In the in-between regime of the Buneman and Pierce instabilities, energetic ions are observed. This effective ion heating is caused by ion detrapping due to double-layer disruption, being consistent with computer simulation. (author)

  5. Switching Fuzzy Guaranteed Cost Control for Nonlinear Networked Control Systems

    Directory of Open Access Journals (Sweden)

    Linqin Cai

    2014-01-01

    Full Text Available This paper deals with the problem of guaranteed cost control for a class of nonlinear networked control systems (NCSs with time-varying delay. A guaranteed cost controller design method is proposed to achieve the desired control performance based on the switched T-S fuzzy model. The switching mechanism is introduced to handle the uncertainties of NCSs. Based on Lyapunov functional approach, some sufficient conditions for the existence of state feedback robust guaranteed cost controller are presented. Simulation results show that the proposed method is effective to guarantee system’s global asymptotic stability and quality of service (QoS.

  6. Hitting probabilities for nonlinear systems of stochastic waves

    CERN Document Server

    Dalang, Robert C

    2015-01-01

    The authors consider a d-dimensional random field u = \\{u(t,x)\\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \\in \\{1,2,3\\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \\beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \\mathbb{R}^d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap

  7. Information Dynamics of a Nonlinear Stochastic Nanopore System

    Directory of Open Access Journals (Sweden)

    Claire Gilpin

    2018-03-01

    Full Text Available Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER and specific entropy rate (SER computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.

  8. Output controllability of nonlinear systems with bounded control

    International Nuclear Information System (INIS)

    Garcia, Rafael; D'Attellis, Carlos

    1990-01-01

    The control problem treated in this paper is the output controllability of a nonlinear system in the form: x = f(x) + g(x)u(t); y = h(x), using bounded controls. The approach to the problem consists of a modification in the system using dynamic feedback in such a way that the input/output behaviour of the closed loop matches the input/output behaviour of a completely output-controllable system with bounded controls. Sufficient conditions are also put forward on the system so that a compact set in the output space may be reached in finite time using uniformally bounded controls, and a result on output regulation in finite time with asymptotic state stabilization is obtained. (Author)

  9. Discrete-Time Nonlinear Control of VSC-HVDC System

    Directory of Open Access Journals (Sweden)

    TianTian Qian

    2015-01-01

    Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.

  10. Analyzing endocrine system conservation and evolution.

    Science.gov (United States)

    Bonett, Ronald M

    2016-08-01

    Analyzing variation in rates of evolution can provide important insights into the factors that constrain trait evolution, as well as those that promote diversification. Metazoan endocrine systems exhibit apparent variation in evolutionary rates of their constituent components at multiple levels, yet relatively few studies have quantified these patterns and analyzed them in a phylogenetic context. This may be in part due to historical and current data limitations for many endocrine components and taxonomic groups. However, recent technological advancements such as high-throughput sequencing provide the opportunity to collect large-scale comparative data sets for even non-model species. Such ventures will produce a fertile data landscape for evolutionary analyses of nucleic acid and amino acid based endocrine components. Here I summarize evolutionary rate analyses that can be applied to categorical and continuous endocrine traits, and also those for nucleic acid and protein-based components. I emphasize analyses that could be used to test whether other variables (e.g., ecology, ontogenetic timing of expression, etc.) are related to patterns of rate variation and endocrine component diversification. The application of phylogenetic-based rate analyses to comparative endocrine data will greatly enhance our understanding of the factors that have shaped endocrine system evolution. Copyright © 2016 Elsevier Inc. All rights reserved.

  11. Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

    Science.gov (United States)

    Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

    2018-04-01

    This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

  12. Oscillating patterns in image processing and nonlinear evolution equations the fifteenth Dean Jacqueline B. Lewis memorial lectures

    CERN Document Server

    Meyer, Yves

    2001-01-01

    Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals. The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics invo...

  13. Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

    Science.gov (United States)

    Agarwal, S.; Wettlaufer, J. S.

    2014-12-01

    We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

  14. Practical application of equivalent linearization approaches to nonlinear piping systems

    International Nuclear Information System (INIS)

    Park, Y.J.; Hofmayer, C.H.

    1995-01-01

    The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA exclamation point s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports

  15. Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

    Science.gov (United States)

    Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

    2015-11-01

    The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

  16. Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

    Science.gov (United States)

    Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

    2018-05-01

    Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

  17. Considering system non-linearity in transmission pricing

    International Nuclear Information System (INIS)

    Oloomi-Buygi, M.; Salehizadeh, M. Reza

    2008-01-01

    In this paper a new approach for transmission pricing is presented. The contribution of a contract on power flow of a transmission line is used as extent-of-use criterion for transmission pricing. In order to determine the contribution of each contract on power flow of each transmission line, first the contribution of each contract on each voltage angle is determined, which is called voltage angle decomposition. To this end, DC power flow is used to compute a primary solution for voltage angle decomposition. To consider the impacts of system non-linearity on voltage angle decomposition, a method is presented to determine the share of different terms of sine argument in sine value. Then the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow using the presented sharing method. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system and the results are analyzed. (author)

  18. Event-Triggered Fault Detection of Nonlinear Networked Systems.

    Science.gov (United States)

    Li, Hongyi; Chen, Ziran; Wu, Ligang; Lam, Hak-Keung; Du, Haiping

    2017-04-01

    This paper investigates the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme. A polynomial fuzzy fault detection filter is designed to generate a residual signal and detect faults in the system. A novel polynomial event-triggered scheme is proposed to determine the transmission of the signal. A fault detection filter is designed to guarantee that the residual system is asymptotically stable and satisfies the desired performance. Polynomial approximated membership functions obtained by Taylor series are employed for filtering analysis. Furthermore, sufficient conditions are represented in terms of sum of squares (SOSs) and can be solved by SOS tools in MATLAB environment. A numerical example is provided to demonstrate the effectiveness of the proposed results.

  19. THz impulse radar for biomedical sensing: nonlinear system behavior

    Science.gov (United States)

    Brown, E. R.; Sung, Shijun; Grundfest, W. S.; Taylor, Z. D.

    2014-03-01

    The THz impulse radar is an "RF-inspired" sensor system that has performed remarkably well since its initial development nearly six years ago. It was developed for ex vivo skin-burn imaging, and has since shown great promise in the sensitive detection of hydration levels in soft tissues of several types, such as in vivo corneal and burn samples. An intriguing aspect of the impulse radar is its hybrid architecture which combines the high-peak-power of photoconductive switches with the high-responsivity and -bandwidth (RF and video) of Schottky-diode rectifiers. The result is a very sensitive sensor system in which the post-detection signal-to-noise ratio depends super-linearly on average signal power up to a point where the diode is "turned on" in the forward direction, and then behaves quasi-linearly beyond that point. This paper reports the first nonlinear systems analysis done on the impulse radar using MATLAB.

  20. Nonlinear Impairment Compensation Using Expectation Maximization for PDM 16-QAM Systems

    DEFF Research Database (Denmark)

    Zibar, Darko; Winther, Ole; Franceschi, Niccolo

    2012-01-01

    We show experimentally that by using non-linear signal processing based algorithm, expectation maximization, nonlinear system tolerance can be increased by 2 dB. Expectation maximization is also effective in combating I/Q modulator nonlinearities and laser linewidth....

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

    International Nuclear Information System (INIS)

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

    1983-01-01

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

  2. Nonlinear control and filtering using differential flatness approaches applications to electromechanical systems

    CERN Document Server

    Rigatos, Gerasimos G

    2015-01-01

    This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...

  3. Artificial boundary conditions for certain evolution PDEs with cubic nonlinearity for non-compactly supported initial data

    Science.gov (United States)

    Vaibhav, V.

    2011-04-01

    The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrödinger (NLS) equation, ∂tu+Lu-iχ|u|2u=0 with L≡-i∂x2, and the equation obtained by letting L≡∂x3. The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness.

  4. Bio-inspired spiking neural network for nonlinear systems control.

    Science.gov (United States)

    Pérez, Javier; Cabrera, Juan A; Castillo, Juan J; Velasco, Juan M

    2018-08-01

    Spiking neural networks (SNN) are the third generation of artificial neural networks. SNN are the closest approximation to biological neural networks. SNNs make use of temporal spike trains to command inputs and outputs, allowing a faster and more complex computation. As demonstrated by biological organisms, they are a potentially good approach to designing controllers for highly nonlinear dynamic systems in which the performance of controllers developed by conventional techniques is not satisfactory or difficult to implement. SNN-based controllers exploit their ability for online learning and self-adaptation to evolve when transferred from simulations to the real world. SNN's inherent binary and temporary way of information codification facilitates their hardware implementation compared to analog neurons. Biological neural networks often require a lower number of neurons compared to other controllers based on artificial neural networks. In this work, these neuronal systems are imitated to perform the control of non-linear dynamic systems. For this purpose, a control structure based on spiking neural networks has been designed. Particular attention has been paid to optimizing the structure and size of the neural network. The proposed structure is able to control dynamic systems with a reduced number of neurons and connections. A supervised learning process using evolutionary algorithms has been carried out to perform controller training. The efficiency of the proposed network has been verified in two examples of dynamic systems control. Simulations show that the proposed control based on SNN exhibits superior performance compared to other approaches based on Neural Networks and SNNs. Copyright © 2018 Elsevier Ltd. All rights reserved.

  5. Nonlinear dynamics analysis of the spur gear system for railway locomotive

    Science.gov (United States)

    Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

    2017-02-01

    Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

  6. Conservation laws for certain time fractional nonlinear systems of partial differential equations

    Science.gov (United States)

    Singla, Komal; Gupta, R. K.

    2017-12-01

    In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.

  7. Effects of error feedback on a nonlinear bistable system with stochastic resonance

    International Nuclear Information System (INIS)

    Li Jian-Long; Zhou Hui

    2012-01-01

    In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing

  8. Controversies regarding evolution of Tax Systems

    Directory of Open Access Journals (Sweden)

    Alia Gabriela DUȚĂ

    2015-09-01

    Full Text Available Originally designed purely to meet the state's financial targets, which were subsequently added as a result of the evolution of human society, a series of economic and social objectives, the tax system is the result of thought, decision and action of the human factor, “expression of the political will of a organized human community, set in a particular territory and having sufficient autonomy to be able, through the bodies they represent, to equip itself with a whole series of legal rules and, in particular tax” .

  9. Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

    Directory of Open Access Journals (Sweden)

    Zhenhua Hu

    2013-01-01

    Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

  10. Evolution of perturbed dynamical systems: analytical computation with time independent accuracy

    Energy Technology Data Exchange (ETDEWEB)

    Gurzadyan, A.V. [Russian-Armenian (Slavonic) University, Department of Mathematics and Mathematical Modelling, Yerevan (Armenia); Kocharyan, A.A. [Monash University, School of Physics and Astronomy, Clayton (Australia)

    2016-12-15

    An analytical method for investigation of the evolution of dynamical systems with independent on time accuracy is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application of the method to complex multi-dimensional Hamiltonian and dissipative systems. It also opens principal opportunities for the qualitative study of chaotic trajectories. The performance of the method is demonstrated on perturbed two-oscillator systems. It can be applied to various non-linear physical and astrophysical systems, e.g. to long-term planetary dynamics. (orig.)

  11. One-Time Pad as a nonlinear dynamical system

    Science.gov (United States)

    Nagaraj, Nithin

    2012-11-01

    The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.

  12. A Highly Accurate Approach for Aeroelastic System with Hysteresis Nonlinearity

    Directory of Open Access Journals (Sweden)

    C. C. Cui

    2017-01-01

    Full Text Available We propose an accurate approach, based on the precise integration method, to solve the aeroelastic system of an airfoil with a pitch hysteresis. A major procedure for achieving high precision is to design a predictor-corrector algorithm. This algorithm enables accurate determination of switching points resulting from the hysteresis. Numerical examples show that the results obtained by the presented method are in excellent agreement with exact solutions. In addition, the high accuracy can be maintained as the time step increases in a reasonable range. It is also found that the Runge-Kutta method may sometimes provide quite different and even fallacious results, though the step length is much less than that adopted in the presented method. With such high computational accuracy, the presented method could be applicable in dynamical systems with hysteresis nonlinearities.

  13. Non-linear and adaptive control of a refrigeration system

    DEFF Research Database (Denmark)

    Rasmussen, Henrik; Larsen, Lars F. S.

    2011-01-01

    are capable of adapting to variety of systems. This paper proposes a novel method for superheat and capacity control of refrigeration systems; namely by controlling the superheat by the compressor speed and capacity by the refrigerant flow. A new low order nonlinear model of the evaporator is developed......In a refrigeration process heat is absorbed in an evaporator by evaporating a flow of liquid refrigerant at low pressure and temperature. Controlling the evaporator inlet valve and the compressor in such a way that a high degree of liquid filling in the evaporator is obtained at all compressor...... capacities ensures a high energy efficiency. The level of liquid filling is indirectly measured by the superheat. Introduction of variable speed compressors and electronic expansion valves enables the use of more sophisticated control algorithms, giving a higher degree of performance and just as important...

  14. On modulated complex non-linear dynamical systems

    International Nuclear Information System (INIS)

    Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.

    1999-01-01

    This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed

  15. Thermal conductivity in one-dimensional nonlinear systems

    Science.gov (United States)

    Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

    2000-03-01

    Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

  16. Nonlinear wave propagation in discrete and continuous systems

    Science.gov (United States)

    Rothos, V. M.

    2016-09-01

    In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.

  17. Nonlinear Quantum Metrology of Many-Body Open Systems

    Science.gov (United States)

    Beau, M.; del Campo, A.

    2017-07-01

    We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.

  18. Nonlinear stochastic systems with incomplete information filtering and control

    CERN Document Server

    Shen, Bo; Shu, Huisheng

    2013-01-01

    Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: ·         a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; ·         new concepts such as random sensor and signal saturations for more realistic modeling; and ·         demonstration of the use of techniques such...

  19. Perturbation methods and closure approximations in nonlinear systems

    International Nuclear Information System (INIS)

    Dubin, D.H.E.

    1984-01-01

    In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

  20. Nonlinear observer designs for fuel cell power systems

    Science.gov (United States)

    Gorgun, Haluk

    A fuel cell is an electrochemical device that combines hydrogen and oxygen, with the aid of electro-catalysts, to produce electricity. A fuel cell consists of a negatively charged anode, a positively charged cathode and an electrolyte, which transports protons or ions. A low temperature fuel cell has an electrical potential of about 0.7 Volt when generating a current density of 300--500 mA/cm2. Practical fuel cell power systems will require a combination of several cells in series (a stack) to satisfy the voltage requirements of specific applications. Fuel cells are suitable for a potentially wide variety of applications, from stationary power generation in the range of hundreds of megawatts to portable electronics in the range of a couple of watts. Efficient operation of a fuel cell system requires advanced feedback control designs. Reliable measurements from the system are necessary to implement such designs. However, most of the commercially available sensors do not operate properly in the reformate and humidified gas streams in fuel cell systems. Sensors working varying degrees of success are too big and costly, and sensors that are potentially low cost are not reliable or do not have the required life time [28]. Observer designs would eliminate sensor needs for measurements, and make feedback control implementable. Since the fuel cell system dynamics are highly nonlinear, observer design is not an easy task. In this study we aim to develop nonlinear observer design methods applicable to fuel cell systems. In part I of the thesis we design an observer to estimate the hydrogen partial pressure in the anode channel. We treat inlet partial pressure as an unknown slowly varying parameter and develop an adaptive observer that employs a nonlinear voltage injection term. However in this design Fuel Processing System (FPS) dynamics are not modelled, and their effect on the anode dynamics are treated as plant uncertainty. In part II of the thesis we study the FPS

  1. Cosmological Evolution of QSO Absorption Systems

    Science.gov (United States)

    Stengler-Larrea, Erik

    1995-08-01

    First, the evolution with cosmic time of the hydrogen clouds which produce the Lyman-alpha absorption lines is studied in dependence on the strength of these lines. From the analysis it is concluded that the results show no evidence of a dependence in the sense of stronger lines evolving faster, although for the resolution at which the used observations were done, it can not be ruled out. Within the same analysis, a distribution of the Doppler parameter of the lines was obtained, with large values and a wide spread. This parameter being an indicator of the gas temperature, this result is in accordance with high temperatures and, consequently, large ionised fractions and a large fraction of the baryonic matter of the universe being associated with these clouds. However, recent high resolution studies seem to reveal that much lower temperatures are characteristic of the clouds. The main content of this thesis, however, focuses on the redshift evolution of the absorbing systems producing absorption at the Lyman limit and of the amount of CIV producing CIV absorption lines. Regarding the CIV absorbers, previous predictions on the effects underlying their redshift distribution pointed to an increase with redshift of the absorbing column densities. In this thesis the first direct measurements of such column densities by profile fitting of a large number of absorption systems (73) are presented, confirming the predictions of a decrease of at least a factor of 3 between z=1.5 and z=3.0. The study on the evolution of Lyman limit absorption systems (LLSs) puts an end to previous discrepancies between the results of different groups. Both a smooth single power law dependence of the LLS number density on redshift indicating no evolution in number density for 0.4 Team of the HST Key Project on QSO absorption lines, and in particular to estimate the necessary exposure times, the magnitudes of several of these objects had to be re-measured. The acquisition of their images and the

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

    Directory of Open Access Journals (Sweden)

    Mingzhu Song

    2016-01-01

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

  3. Dynamics of atom-field probability amplitudes in a coupled cavity system with Kerr non-linearity

    Energy Technology Data Exchange (ETDEWEB)

    Priyesh, K. V.; Thayyullathil, Ramesh Babu [Department of Physics, Cochin University of Science and Technology, Cochin (India)

    2014-01-28

    We have investigated the dynamics of two cavities coupled together via photon hopping, filled with Kerr non-linear medium and each containing a two level atom in it. The evolution of various atom (field) state probabilities of the coupled cavity system in two excitation sub space are obtained numerically. Detailed analysis has been done by taking different initial conditions of the system, with various coupling strengths and by varying the susceptibility of the medium. The role of susceptibility factor, on the dynamics atom field probability has been examined. In a coupled cavity system with strong photon hopping it is found that the susceptibility factor modifies the behaviour of probability amplitudes.

  4. Dispersion and nonlinear effects in OFDM-RoF system

    Science.gov (United States)

    Alhasson, Bader H.; Bloul, Albe M.; Matin, M.

    2010-08-01

    The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.

  5. A general sensitivity theory for simulations of nonlinear systems

    International Nuclear Information System (INIS)

    Kenton, M.A.

    1981-01-01

    A general sensitivity theory is developed for nonlinear lumped-parameter system simulations. The point-of-departure is general perturbation theory, which has long been used for linear systems in nuclear engineering and reactor physics. The theory allows the sensitivity of particular figures-of-merit of the system behavior to be calculated with respect to any parameter.An explicit procedure is derived for applying the theory to physical systems undergoing sudden events (e.g., reactor scrams, tank ruptures). A related problem, treating figures-of-merit defined as functions of extremal values of system variables occurring at sudden events, is handled by the same procedure. The general calculational scheme for applying the theory to numerical codes is discussed. It is shown that codes which use pre-packaged implicit integration subroutines can be augmented to include sensitivity theory: a companion set of subroutines to solve the sensitivity problem is listed. This combined system analysis code is applied to a simple model for loss of post-accident heat removal in a liquid metal-cooled fast breeder reactor. The uses of the theory for answering more general sensitivity questions are discussed. One application of the theory is to systematically determine whether specific physical processes in a model contribute significantly to the figures-of-merit. Another application of the theory is for selecting parameter values which enable a model to match experimentally observed behavior

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

    International Nuclear Information System (INIS)

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

    2003-01-01

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

  7. Brand Equity Evolution: a System Dynamics Model

    Directory of Open Access Journals (Sweden)

    Edson Crescitelli

    2009-04-01

    Full Text Available One of the greatest challenges in brand management lies in monitoring brand equity over time. This paper aimsto present a simulation model able to represent this evolution. The model was drawn on brand equity concepts developed by Aaker and Joachimsthaler (2000, using the system dynamics methodology. The use ofcomputational dynamic models aims to create new sources of information able to sensitize academics and managers alike to the dynamic implications of their brand management. As a result, an easily implementable model was generated, capable of executing continuous scenario simulations by surveying casual relations among the variables that explain brand equity. Moreover, the existence of a number of system modeling tools will allow extensive application of the concepts used in this study in practical situations, both in professional and educational settings

  8. Nonlinear analysis of a rotor-bearing system using describing functions

    Science.gov (United States)

    Maraini, Daniel; Nataraj, C.

    2018-04-01

    This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

  9. Exploring lipids with nonlinear optical microscopy in multiple biological systems

    Science.gov (United States)

    Alfonso-Garcia, Alba

    Lipids are crucial biomolecules for the well being of humans. Altered lipid metabolism may give rise to a variety of diseases that affect organs from the cardiovascular to the central nervous system. A deeper understanding of lipid metabolic processes would spur medical research towards developing precise diagnostic tools, treatment methods, and preventive strategies for reducing the impact of lipid diseases. Lipid visualization remains a complex task because of the perturbative effect exerted by traditional biochemical assays and most fluorescence markers. Coherent Raman scattering (CRS) microscopy enables interrogation of biological samples with minimum disturbance, and is particularly well suited for label-free visualization of lipids, providing chemical specificity without compromising on spatial resolution. Hyperspectral imaging yields large datasets that benefit from tailored multivariate analysis. In this thesis, CRS microscopy was combined with Raman spectroscopy and other label-free nonlinear optical techniques to analyze lipid metabolism in multiple biological systems. We used nonlinear Raman techniques to characterize Meibum secretions in the progression of dry eye disease, where the lipid and protein contributions change in ratio and phase segregation. We employed similar tools to examine lipid droplets in mice livers aboard a spaceflight mission, which lose their retinol content contributing to the onset of nonalcoholic fatty-liver disease. We also focused on atherosclerosis, a disease that revolves around lipid-rich plaques in arterial walls. We examined the lipid content of macrophages, whose variable phenotype gives rise to contrasting healing and inflammatory activities. We also proposed new label-free markers, based on lifetime imaging, for macrophage phenotype, and to detect products of lipid oxidation. Cholesterol was also detected in hepatitis C virus infected cells, and in specific strains of age-related macular degeneration diseased cells by

  10. On nonlinear control design for autonomous chaotic systems of integer and fractional orders

    International Nuclear Information System (INIS)

    Ahmad, Wajdi M.; Harb, Ahmad M.

    2003-01-01

    In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

  11. Fault Diagnosis of Nonlinear Systems Using Structured Augmented State Models

    Institute of Scientific and Technical Information of China (English)

    Jochen Aβfalg; Frank Allg(o)wer

    2007-01-01

    This paper presents an internal model approach for modeling and diagnostic functionality design for nonlinear systems operating subject to single- and multiple-faults. We therefore provide the framework of structured augmented state models. Fault characteristics are considered to be generated by dynamical exosystems that are switched via equality constraints to overcome the augmented state observability limiting the number of diagnosable faults. Based on the proposed model, the fault diagnosis problem is specified as an optimal hybrid augmented state estimation problem. Sub-optimal solutions are motivated and exemplified for the fault diagnosis of the well-known three-tank benchmark. As the considered class of fault diagnosis problems is large, the suggested approach is not only of theoretical interest but also of high practical relevance.

  12. Online prediction and control in nonlinear stochastic systems

    DEFF Research Database (Denmark)

    Nielsen, Torben Skov

    2002-01-01

    speed and the relationship between (primarily) wind speed and wind power (the power curve). In paper G the model parameters are estimated using a RLS algorithm and any systematic time-variation of the model parameters is disregarded. Two di erent parameterizations of the power curve is considered...... are estimated using the algorithm proposed in paper C. The power curve and the diurnal variation of wind speed is estimated separately using the local polynomial regression procedure described in paper A . In paper J the parameters of the prediction model is assumed to be smooth functions of wind direction (and......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...

  13. Distributed Synchronization Control of Multiagent Systems With Unknown Nonlinearities.

    Science.gov (United States)

    Su, Shize; Lin, Zongli; Garcia, Alfredo

    2016-01-01

    This paper revisits the distributed adaptive control problem for synchronization of multiagent systems where the dynamics of the agents are nonlinear, nonidentical, unknown, and subject to external disturbances. Two communication topologies, represented, respectively, by a fixed strongly-connected directed graph and by a switching connected undirected graph, are considered. Under both of these communication topologies, we use distributed neural networks to approximate the uncertain dynamics. Decentralized adaptive control protocols are then constructed to solve the cooperative tracker problem, the problem of synchronization of all follower agents to a leader agent. In particular, we show that, under the proposed decentralized control protocols, the synchronization errors are ultimately bounded, and their ultimate bounds can be reduced arbitrarily by choosing the control parameter appropriately. Simulation study verifies the effectiveness of our proposed protocols.

  14. Nonlinear transport behavior of low dimensional electron systems

    Science.gov (United States)

    Zhang, Jingqiao

    The nonlinear behavior of low-dimensional electron systems attracts a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. In response to microwave radiation and dc bias, strongly nonlinear electron transport that gives rise to unusual electron states has been reported in two-dimensional systems of electrons in high magnetic fields. There has also been great interest in the nonlinear response of quantum ballistic constrictions, where the effects of quantum interference, spatial dispersion and electron-electron interactions play crucial roles. In this thesis, experimental results of the research of low dimensional electron gas systems are presented. The first nonlinear phenomena were observed in samples of highly mobile two dimensional electrons in GaAs heavily doped quantum wells at different magnitudes of DC and AC (10 KHz to 20 GHz) excitations. We found that in the DC excitation regime the differential resistance oscillates with the DC current and external magnetic field, similar behavior was observed earlier in AlGaAs/GaAs heterostructures [C.L. Yang et al. ]. At external AC excitations the resistance is found to be also oscillating as a function of the magnetic field. However the form of the oscillations is considerably different from the DC case. We show that at frequencies below 100 KHz the difference is a result of a specific average of the DC differential resistance during the period of the external AC excitations. Secondly, in similar samples, strong suppression of the resistance by the electric field is observed in magnetic fields at which the Landau quantization of electron motion occurs. The phenomenon survives at high temperatures at which the Shubnikov de Haas oscillations are absent. The scale of the electric fields essential for the effect, is found to be proportional to temperature in the low temperature limit. We suggest that the strong reduction of the longitudinal resistance

  15. Reproduction of Economic Interests as a Nonlinear Dynamical System

    Directory of Open Access Journals (Sweden)

    Smiesova Viktoria L.

    2017-12-01

    Full Text Available The aim of the article is to define the system characteristics of reproduction of economic interests of actors, substantiate the possibility of its evolutionary and revolutionary development and the nonlinearity of its development in dynamics. The article justifies the main characteristics of the system of reproduction of economic interests. It is proved that in this system stability and variability are complementarily combined as integrated mechanisms of its development in statics and dynamics, assurance of its self-organization and self-restoration, quantitative and qualitative transformation. In its static state, there prevail characteristics of steadiness and leaning towards stability and constancy. In the dynamic state, the main characteristic is variability of the system of reproduction of economic interests, which determines / reacts to the processes of transformation and development of its constituent subsystems, potential opportunities, preferences and economic behavior of actors (changes in the endogenous environment, institutions and establishments, constraints and stabilizers (changes in the exogenous environment. The model of dynamic development of the system for reproduction of economic interests is proposed, the phases of its evolutionary and revolutionary development are substantiated.

  16. Linear homotopy solution of nonlinear systems of equations in geodesy

    Science.gov (United States)

    Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.

    2010-01-01

    A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.

  17. Nonlinear oscillation system of mass with serial linear and nonlinear springs

    DEFF Research Database (Denmark)

    Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S

    2013-01-01

    In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...... alternatives to overcome the difficulty of capturing the periodic behavior of the solution, as the most evident characteristic of oscillators. It can be clearly observed that approximate frequencies and periodic solutions are in excellent agreement with the exact ones. First approximation leads to high...

  18. Controlling wave propagation through nonlinear engineered granular systems

    Science.gov (United States)

    Leonard, Andrea

    We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave

  19. Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

    Science.gov (United States)

    Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

  20. A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems

    Science.gov (United States)

    Stavrou, D.; Duit, R.; Komorek, M.

    2008-01-01

    A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…