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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.
List of contents
Introduction to Nonlinear Dynamical Systems.- Nonlinear Chaos and Multifractality.- Nonlinear Discrete Dynamical Systems.- Switching Dynamical Systems.- Mapping dynamics, symmetry and attractor fragementation.- Appendix A. Linear dynamical systems.- Appendix B. Discrete Linear dynamical systems.
Summary
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.
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From the reviews:
“The aim of this book is to provide a basis and a survey of the main topics the author’s research is devoted to. … The first and second chapters of the book contain the nonlinear counterpart of the theory for continuous and discrete dynamical systems. … These two first chapters together with the two appendices conform a textbook for an undergraduate student.” (Maite Grau, Zentralblatt MATH, Vol. 1253, 2013)
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From the reviews:
"The aim of this book is to provide a basis and a survey of the main topics the author's research is devoted to. ... The first and second chapters of the book contain the nonlinear counterpart of the theory for continuous and discrete dynamical systems. ... These two first chapters together with the two appendices conform a textbook for an undergraduate student." (Maite Grau, Zentralblatt MATH, Vol. 1253, 2013)
