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About this book

This book describes systematic design techniques for chaotic and hyperchaotic systems, the transition from one to the other, and their implementation in electronic circuits. It also discusses the collective phenomena manifested by these systems when connected by a physical coupling scheme. Readers will be introduced to collective behaviours, such as synchronization and oscillation suppression, and will learn how to implement nonlinear differential equations in electronic circuits.

Further, the book shows how the choice of nonlinearity can lead to chaos and hyperchaos, even in a first-order time-delayed system. The occurrence of these phenomena, together with the efficiency of the design techniques described, is presented with theoretical studies, numerical characterization and experimental demonstrations with the corresponding electronic circuits, helping readers grasp the design aspects of dynamical systems as a whole in electronic circuits. The authors then discuss the usefulness of an active all-pass filter as the delay element, supported by their own experimental observations, as well as theoretical and numerical results.

Including detailed analysis, as well as computations with suitable dedicated software packages, the book will be of interest to all academics and researchers who wish to expand their knowledge of the subtlety of nonlinear time-delayed systems. It also offers a valuable source of information for engineers, linking the design techniques of chaotic time-delayed systems with their collective phenomena.

Table of Contents


Chapter 1. Introduction

For the last few decades, much emphasis has been imposed on exploring the dynamics of systems having intrinsic time delays.
Debabrata Biswas, Tanmoy Banerjee

Chapter 2. First-Order Time-Delayed Chaotic Systems: Design and Experiment

In this chapter, we discuss the design principle of chaotic time-delayed systems with (i) a bimodal nonlinearity and (ii) an unimodal nonlinearity.
Debabrata Biswas, Tanmoy Banerjee

Chapter 3. Chaotic Time-Delayed System with Hard Nonlinearity: Design and Characterization

In Chap. 2, we have discussed two chaotic time-delayed systems.
Debabrata Biswas, Tanmoy Banerjee

Chapter 4. Collective Behavior-I: Synchronization in Hyperchaotic Time-Delayed Oscillators Coupled Through a Common Environment

Collective behaviors of coupled dynamical systems are of significant interest in the field of physical and biological sciences, and engineering [96]. The prominent collective behaviors that occur in periodic and chaotic systems are synchronization and phase locking [96], oscillation suppression [10, 15, 16, 47, 63, 112], chimera states [9, 91, 113], etc. We have already discussed in Chap. 1 that synchronization of chaos in time-delayed chaotic system was reported much later by Pyragas [100] (1998) than its discovery in low-dimensional chaotic systems [93] (in 1990). In all the research works discussed in Chap. 1 (Sect. 1.2, p. 6), the coupling schemes were essentially the direct coupling, i.e., either unidirectional coupling or bidirectional coupling , where either of the two coupled systems or both the systems directly affect the dynamics of each other.
Debabrata Biswas, Tanmoy Banerjee

Chapter 5. Collective Behavior-II: Amplitude Death and the Corresponding Transitions in Coupled Chaotic Time-Delayed Systems

In the previous chapter (Chap. 4), we have discussed synchronization scenarios in time-delayed systems.
Debabrata Biswas, Tanmoy Banerjee

Chapter 6. Epilogue: Future Directions

Dynamics of nonlinear time-delayed systems is a broad subject. In this brief, we only covered two specific topics: design of time-delayed chaos generators and their collective behaviors.
Debabrata Biswas, Tanmoy Banerjee


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