Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques. This book also: Presents novel concepts and methods for dynamical system synchronization Extends beyond the Lyapunov theory for dynamical system synchronization Introduces companion and synchronization of discrete dynamical systemsIncludes local singularity theory for discontinuous dynamical systems Covers the invariant domains of synchronizationFeatures more than 75 illustrationsDynamical System Synchronization is an ideal book for those interested in better understanding new concepts and methodology for dynamical system synchronization, local singularity theory for discontinuous dynamical systems, distinct dynamical system synchronization, and invariant domains of synchronization. Read more... Introduction -- Discontinuity and Local Singularity -- Single Constraint Synchronization -- Multiple Constraints Synchronization -- Function Synchronizations -- Discrete Systems Synchronization Cover 1 Dynamical System Synchronization 4 Preface 6 Contents 8 Chapter 1: Introduction 10 1.1 A Brief History 11 1.2 Book Layout 14 References 15 Chapter 2: Discontinuity and Local Singularity 19 2.1 Discontinuous Dynamical Systems 19 2.2 G-Functions 23 2.3 Passable Flows 27 2.4 Non-passable Flows 34 2.5 Grazing Flows 48 2.6 Flow Switching Bifurcations 61 References 77 Chapter 3: Single Constraint Synchronization 78 3.1 Introduction to Synchronization 78 3.1.1 Generalized Synchronization 84 3.1.2 Resultant Dynamical Systems 86 3.2 Synchronization with a Single Constraint 90 3.2.1 Synchronicity 90 3.2.2 Singularity to Constraint 94 3.3 Synchronicity with Singularity 98 3.4 Higher Order Singularity 99 3.5 Synchronization to Constraint 103 3.6 Desynchronization to Constraint 118 3.7 Penetration to Constraint 124 References 127 Chapter 4: Multiple Constraints Synchronization 128 4.1 Synchronicity to Multiple Constraints 128 4.2 Singularity to Constraints 131 4.3 Synchronicity with Singularity to Constraints 134 4.4 Higher-Order Singularity to Constraints 137 4.5 Synchronization to All Constraints 140 4.6 Desynchronization to All Constraints 145 4.7 Penetration to All Constraints 149 4.8 Synchronization-Desynchronization-Penetration 152 4.9 Complexity by System Synchronization 158 References 162 Chapter 5: Function Synchronizations 163 5.1 Synchronization Constraints 163 5.2 Synchronization Mechanism 165 5.3 Sinusoidal Synchronization 172 5.3.1 Synchronization Dynamics 177 5.3.2 Sinusoidal Synchronization of Chaotic Motions 184 5.3.3 Sinusoidal Synchronizations of Periodic Motions 188 References 200 Chapter 6: Discrete Systems Synchronization 202 6.1 Discrete Systems with a Single Nonlinear Map 202 6.2 Discrete Systems with Multiple Maps 208 6.3 Complete Dynamics of a Henon Map System 212 6.4 Companion and Synchronization 218 6.5 An Application of Discrete Systems Synchronization 234 References 241 Index 6 Dynamical System Synchronization (dss) Meticulously Presents For The First Time The Theory Of Dynamical Systems Synchronization Based On The Local Singularity Theory Of Discontinuous Dynamical Systems. The Book Details The Sufficient And Necessary Conditions For Dynamical Systems Synchronizations, Through Extensive Mathematical Expression. Techniques For Engineering Implementation Of Dss Are Clearly Presented Compared With The Existing Techniques. This Book Also: Presents Novel Concepts And Methods For Dynamical System Synchronization, Extends Beyond The Lyapunov Theory For Dynamical System Synchronization, Introduces Companion And Synchronization Of Discrete Dynamical Systems, Includes Local Singularity Theory For Discontinuous Dynamical Systems, Covers The Invariant Domains Of Synchronization, Features More Than 75 Illustrations. Dynamical System Synchronization Is An Ideal Book For Those Interested In Better Understanding New Concepts And Methodology For Dynamical System Synchronization, Local Singularity Theory For Discontinuous Dynamical Systems, Distinct Dynamical System Synchronization, And Invariant Domains Of Synchronization.
