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Author Lakshmanan, M. (Muthusamy)
Title Dynamics of nonlinear time-delay systems / M. Lakshmanan, D.V. Senthilkumar.
Imprint Berlin ; Heidelberg ; New York : Springer, 2010.

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Author Lakshmanan, M. (Muthusamy)
Series Springer series in synergetics
Springer complexity
Springer series in synergetics.
Springer complexity.
Subject Time delay systems -- Dynamics.
Nonlinear systems.
Alt Name Senthilkumar, D. V. (Dharmapuri Vijayan)
Description 1 online resource (xvii, 313 pages) : illustrations
Bibliography Note Includes bibliographical references and index.
Contents Cover -- Preface -- Contents -- Chapter 1 Delay Differential Equations -- 1.1 Introduction -- 1.1.1 DDE with Single Constant Delay -- 1.1.2 DDE with Discrete Delays -- 1.1.3 DDE with Distributed Delay -- 1.1.4 DDE with State-Dependent Delay -- 1.1.5 DDE with Time-Dependent Delay -- 1.2 Constructing the Solution for DDEs with Single Constant Delay -- 1.2.1 Linear Delay Differential Equation -- 1.2.2 Numerical Simulation of DDEs -- 1.2.3 Nonlinear Delay Differential Equations -- 1.3 Salient Features of Chaotic Time-Delay Systems -- References -- Chapter 2 Linear Stability and Bifurcation Analysis -- 2.1 Introduction -- 2.2 Linear Stability Analysis -- 2.2.1 Example: Linear Delay Differential Equation -- 2.3 A Geometric Approach to Study Stability -- 2.3.1 Example: Linear Delay Differential Equation -- 2.4 A General Approach to Determine Linear Stability of Equilibrium Points -- 2.4.1 Characteristic Equation -- 2.4.2 Stability Conditions -- 2.4.3 Stability Curves/Surfaces in the (, a, b) Parameter Space -- 2.4.4 Extension to Coupled DDEs/Complex Scalar DDEs -- 2.4.5 Bifurcation Analysis -- 2.4.6 Results of Stability Analysis -- 2.4.7 A Theorem on the Stability of Equilibrium Points -- 2.4.8 Example: Linear Delay Differential Equation -- References -- Chapter 3 Bifurcation and Chaos in Time-Delayed Piecewise Linear Dynamical System -- 3.1 Introduction -- 3.2 Simple Scalar First Order Piecewise Linear DDE -- 3.2.1 Fixed Points and Linear Stability -- 3.3 Numerical Study of the Single Scalar Piecewise Linear Time-Delay System -- 3.3.1 Dynamics in the Pseudospace -- 3.3.2 Transients -- 3.3.3 One and Two Parameter Bifurcation Diagrams -- 3.3.4 Lyapunov Exponents and Hyperchaotic Regimes -- 3.4 Experimental Realization using PSPICE Simulation -- 3.5 Stability Analysis and Chaotic Dynamics of Coupled DDEs -- 3.5.1 Fixed Points and Linear Stability -- 3.6 Numerical Analysis of the Coupled DDE -- 3.6.1 Transients -- 3.6.2 One and Two Parameter Bifurcation Diagrams -- References -- Chapter 4 A Few Other Interesting Chaotic Delay Differential Equations -- 4.1 Introduction -- 4.2 The Mackey-Glass System: A Typical Nonlinear DDE -- 4.2.1 Mackey-Glass Time-Delay System -- 4.2.2 Fixed Points and Linear Stability Analysis -- 4.2.3 Time-Delay =0 -- 4.2.4 Time-Delay>0 -- 4.2.5 Numerical Simulation: Bifurcations and Chaos -- 4.2.6 Experimental Realization Using Electronic Circuit -- 4.3 Other Interesting Scalar Chaotic Time-Delay Systems -- 4.3.1 A Simple Chaotic Delay Differential Equation -- 4.3.2 Ikeda Time-Delay System -- 4.3.3 Scalar Time-Delay System with Polynomial Nonlinearity -- 4.3.4 Scalar Time-Delay System with Other Piecewise Linear Nonlinearities -- 4.3.5 Another Form of Scalar Time-Delay System -- 4.3.6 El Ni241;o and the Delayed Action Oscillator -- 4.4 Coupled Chaotic Time-Delay Systems -- 4.4.1 Time-Delayed Chua's Circuit -- 4.4.2 Semiconductor Lasers -- 4.4.3 Neural Networks -- References -- Chapter 5 Implications of Delay Feedback: Amplitude Death and Other Effects -- 5.1 Introduction -- 5.2 Time-Delay Induced Amplitude Death -- 5.2.1 Theoretical Study: Single Oscillator -- 5.2.2 Experimental Study -- 5.3 Amplitude Death with Distributed Delay in Coupled Limit Cycle Oscillators -- 5.4 Amplitude Death in Coupled Chaotic Oscillators -- 5.5 Amplitude.
Note Print version record.
Summary 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 lengthsof 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 branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.
ISBN 9783642149382 (electronic bk.)
3642149383 (electronic bk.)
3642149375 (print)
9783642149375 (print)
ISBN/ISSN 10.1007/978-3-642-14938-2
978-3-642-14938-2 Springer
OCLC # 701718785
Additional Format Print version: Lakshmanan, M. (Muthusamy). Dynamics of nonlinear time-delay systems. Berlin : Springer-Verlag, 2010 (DLC) 2010936895

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