Regularity and Complexity in Dynamical Systems

Regularity and Complexity in Discontinuous Dynamical Systems describes periodic and chaotic behaviors in discontinuous dynamical systems, including 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 extensively exist 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 discusses new concepts in discontinuous dynamical systems and the smoothening of discontinuity misleading dynamical behaviors. In addition, it shows transports and switching of discontinuous dynamical systems and the mechanism of chaos and diffusion in impulsive systems. It also shows symmetry and strange attractor fragmentation.