Dynamical Systems: Theories and Applications

ISBN-13: 9780367137045 / Angielski / Twarda / 2019 / 400 str.

Zeraoulia Elhadj

Opis

This book presents the latest investigations in the theory of chaotic systems and their dynamics. It covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. The book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.

Spis treści

Contents

Review of Chaotic Dynamics

Introduction

Poincare map technique

Smale horseshoe

Symbolic dynamics

Strange attractors

Basins of attraction

Density, robustness and persistence of chaos

Entropies of chaotic attractors

Period 3 implies chaos

The Snap-back repeller and the Li-Chen-Marotto theorem

Shi'lnikov criterion for the existence of chaos

　

Human Immunodeficiency Virus and Urbanization Dynamics

Introduction

Definition of Human Immunodeficiency Virus (HIV)

Modelling the Human Immunodeficiency Virus (HIV)

Dynamics of sexual transmission of the Human Immunodeficiency Virus

The effects of variable infectivity on the HIV dynamics

The CD4+ Lymphocyte dynamics in HIV infection

The viral dynamics of a highly pathogenic simian/human immunodeficiency virus

The effects of morphine on Simian Immunodeficiency Virus Dynamics

The dynamics of the HIV therapy system

Dynamics of urbanization

　

Chaotic Behaviors in Piecewise Linear Mappings

Introduction

Chaos in one-dimensional piecewise smooth maps

Chaos in one-dimensional singular maps

Chaos in 2-D piecewise smooth maps

　

Robust Chaos in Neural Networks Models

Introduction

Chaos in neural networks models

Robust chaos in discrete time neural networks

The importance of robust chaos in mathematics and some open problems

　

Estimating Lyapunouv Exponents of 2-D Discrete Mappings

Introduction

Lyapunouv exponents of the discrete hyperchaotic double scroll map

Lyapunouv exponents for a class of 2-D piecewise linear mappings

Lyapunouv exponents of a family of 2-D discrete mappings with separate variables

Lyapunouv exponents of a discontinuous piecewise linear mapping of the plane governed by a simple switching law

Lyapunouv exponents of a modified map-based BVP model

　

Control, Synchronization and Chaotification of Dynamical Systems

Introduction

Compound synchronization of different chaotic systems

Synchronization of 3-D continuous-time quadratic systems using a universal nonlinear control law

Co-existence of certain types of synchronization and its inverse

Synchronization of 4-D continuous-time quadratic systems using a universal nonlinear control law

Quasi-synchronization of systems with different dimension

Chaotification of 3-D linear continuous-time systems using the signum function feedback

Chaos control problem of a 3-D cancer model with structured uncertainties

Controlling homoclinic chaotic attractor

Robustification of 2-D piecewise smooth mappings

Chaotifying stable n-D linear maps via the controller of any bounded function

　

　

　

Boundedness of Some Forms of Quadratic Systems

Introduction

Boundedness of certain forms of 3-D quadratic continuous-time systems

Bounded jerky dynamics

Bounded hyperjerky dynamics

Boundedness of the generalized 4-D hyperchaotic model containing Lorenz-Steno and Lorenz-Haken systems

Boundedness of 2-D Henon-like mapping

Examples of fully bounded chaotic attractors

　

Some Forms of Globally Asymptotically Stable Attractors

Introduction

Direct Lyapunov stability for ordinary differential equations

Exponential stability of nonlinear time-varying

Lasalle's Invariance Principle

Direct Lyapunov-type stability for fractional-like systems

Construction of globally asymptotically stable n-D discrete mappings

Construction of superstable n-D mappings

Examples of globally superstable 1-D quadratic mappings

Construction of globally superstable 3-D quadratic mappings

Hyperbolicity of dynamical systems

Consequences of uniform hyperbolicity

Structural stability for 3-D quadratic mappings

Construction of globally asymptotically stable partial differential systems

Construction of globally stable system of delayed differential equations

Stabilization by the Jurdjevic-Quinn method

　

Transformation of Dynamical Systems to Hyperjerky Motions

Introduction

Transformation of 3-D dynamical systems to jerk form

Transformation of 3-D dynamical systems to rational and cubic jerks forms

Transformation of 4-D dynamical systems to hyperjerk form

Examples of crackle and top dynamics

　

Bibliography

Index