Dynamics of Nonlinear Time-Delay Systems

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.