TUM Library

Cover; Title Page; Copyright Page; Preface; Table of Contents; Preface; 1: Review of Chaotic Dynamics; 1.1 Introduction; 1.2 Poincaré map technique; 1.3 Smale horseshoe; 1.4 Symbolic dynamics; 1.5 Strange attractors; 1.6 Basins of attraction; 1.7 Density, robustness and persistence of chaos; 1.8 Entropies of chaotic attractors; 1.9 Period 3 implies chaos; 1.10 The Snap-back repeller and the Li-Chen-Marotto theorem; 1.11 Shilnikov criterion for the existence of chaos; 2: Human Immunodeficiency Virus and Urbanization Dynamics; 2.1 Introduction

2.2 Definition of Human Immunodeficiency Virus (HIV)2.3 Modelling the Human Immunodeficiency Virus (HIV); 2.4 Dynamics of sexual transmission of the Human Immunodeficiency Virus; 2.5 The effects of variable infectivity on the HIV dynamics; 2.6 The CD4+ Lymphocyte dynamics in HIV infection; 2.7 The viral dynamics of a highly pathogenic Simian/Human Immunodeficiency Virus; 2.8 The effects of morphine on Simian Immunodeficiency Virus Dynamics; 2.9 The dynamics of the HIV therapy system; 2.10 Dynamics of urbanization; 3: Chaotic Behaviors in Piecewise Linear Mappings; 3.1 Introduction

3.2 Chaos in one-dimensional piecewise smooth maps3.3 Chaos in one-dimensional singular maps; 3.4 Chaos in 2-D piecewise smooth maps; 4: Robust Chaos in Neural Networks Models; 4.1 Introduction; 4.2 Chaos in neural networks models; 4.3 Robust chaos in discrete time neural networks; 4.3.1 Robust chaos in 1-D piecewise-smooth neural networks; 4.3.2 Fragile chaos (blocks with smooth activation function); 4.3.3 Robust chaos (blocks with non-smooth activation function); 4.3.4 Robust chaos in the electroencephalogram model; 4.3.5 Robust chaos in Diluted circulant networks

4.3.6 Robust chaos in non-smooth neural networks4.4 The importance of robust chaos in mathematics and some open problems; 5: Estimating Lyapunov Exponents of 2-D Discrete Mappings; 5.1 Introduction; 5.2 Lyapunov exponents of the discrete hyperchaotic double scroll map; 5.3 Lyapunov exponents for a class of 2-D piecewise linear mappings; 5.4 Lyapunov exponents of a family of 2-D discrete mappings with separate variables; 5.5 Lyapunov exponents of a discontinuous piecewise linear mapping of the plane governed by a simple switching law; 5.6 Lyapunov exponents of a modified map-based BVP model

6: Control, Synchronization and Chaotification of Dynamical Systems6.1 Introduction; 6.2 Compound synchronization of different chaotic systems; 6.3 Synchronization of 3-D continuous-time quadratic systems using a universal non-linear control law; 6.4 Co-existence of certain types of synchronization and its inverse; 6.5 Synchronization of 4-D continuous-time quadratic systems using a universal non-linear control law; 6.6 Quasi-synchronization of systems with different dimensions; 6.7 Chaotification of 3-D linear continuous-time systems using the signum function feedback

Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.

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