Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive,discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually,the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems. This book also: - Illustrates new concepts and methodology in discontinuous dynamical systems Uses different ideas to describe complicated dynamical systems in real worlds Discuss the complete dynamics and the corresponding YingYang theory as well as complexity and factuality of chaos in dynamical systems Discusses the mechanism of chaos and diffusion in impulsive systems Discusses strange attractor fragmentation and hidden mathematical structures Contains intuitive illustrations and systematical description as well as complete example demonstrations Regularity and Complexity in Dynamical Systems is an ideal book for those interested in better understanding complexity and chaos caused by nonlinearity, discontinuity, switching, and impulses.
Nonlinear Continuous Dynamical Systems.- Nonlinear Discrete Dynamical Systems.- Chaos and Multifractality.- Complete Dynamics and Synchronization.- Switching Dynamical Systems.- Mapping Dynamics and Symmetry.- Appendix A. Linear Continuous Dynamical Systems.- Appendix B. Linear Discrete Dynamical Systems.