Overview
- Presents a theory and mathematical methods for discontinuous dynamical systems
- Provides useful mathematical tools to describe the natural complexity in practical dynamical systems
- Presents a theory for dynamical systems with flow barriers for the first time
- Challenges current existing theories of dynamical systems under Lipschitz conditions
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
“Discontinuous Dynamical Systems” presents a theory of dynamics and flow switchability in discontinuous dynamical systems, which can be as the mathematical foundation for a new dynamics of dynamical system networks. The book includes a theory for flow barriers and passability to boundaries in discontinuous dynamical systems that will completely change traditional concepts and ideas in the field of dynamical systems. Edge dynamics and switching complexity of flows in discontinuous dynamical systems are explored in the book and provide the mathematical basis for developing the attractive network channels in dynamical systems. The theory of bouncing flows to boundaries, edges and vertexes in discontinuous dynamical systems with multi-valued vector fields is described in the book as a “billiard” theory of dynamical system networks. The theory of dynamical system interactions in discontinued dynamical systems can be used as a general principle in dynamical system networks, which is applied to dynamical system synchronization.
The book represents a valuable reference work for university professors and researchers in applied mathematics, physics, mechanics, and control.
Dr. Albert C.J. Luo is an internationally respected professor in nonlinear dynamics and mechanics, and he works at Southern Illinois University Edwardsville, USA.
Reviews
From the reviews:
“I highly recommend this book to both scientists and researchers as well as to university teachers and students with an interest in discontinuous dynamical systems, and I believe that the author has succeeded quite admirably with this book. … one of the first books that comprehensively discusses discontinuous dynamical systems and develops a theoretical framework in discontinuous dynamical systems.” (Marius-Florin Danca, Mathematical Reviews, September, 2013)Authors and Affiliations
Bibliographic Information
Book Title: Discontinuous Dynamical Systems
Authors: Albert C. J. Luo
DOI: https://doi.org/10.1007/978-3-642-22461-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Higher Education Press,Beijing and Springer-Verlag GmbH Berlin Heidelberg 2012
eBook ISBN: 978-3-642-22461-4Published: 07 April 2012
Edition Number: 1
Number of Pages: XI, 692
Number of Illustrations: 50 b/w illustrations, 170 illustrations in colour
Additional Information: Jointly published with Higher Education Press
Topics: Systems Theory, Control, Applications of Nonlinear Dynamics and Chaos Theory, Vibration, Dynamical Systems, Control