Overview
- Presents monotonic and oscillatory stability and bifurcations in nonlinear discrete systems
- Provides different perspectives on nonlinear discrete systems, to help readers better understand the nonlinear dynamics of such systems
- Discusses infinite-fixed-point discrete systems in local analysis for the first time
Part of the book series: Nonlinear Physical Science (NPS)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents(5 chapters)
About this book
This book focuses on bifurcation and stability in nonlinear discrete systems, including monotonic and oscillatory stability. It presents the local monotonic and oscillatory stability and bifurcation of period-1 fixed-points on a specific eigenvector direction, and discusses the corresponding higher-order singularity of fixed-points. Further, it explores the global analysis of monotonic and oscillatory stability of fixed-points in 1-dimensional discrete systems through 1-dimensional polynomial discrete systems. Based on the Yin-Yang theory of nonlinear discrete systems, the book also addresses the dynamics of forward and backward nonlinear discrete systems, and the existence conditions of fixed-points in said systems. Lastly, in the context of local analysis, it describes the normal forms of nonlinear discrete systems and infinite-fixed-point discrete systems. Examining nonlinear discrete systems from various perspectives, the book helps readers gain a better understanding of the nonlinear dynamics of such systems.
Authors and Affiliations
-
Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, USA
Albert C. J. Luo
About the author
Prof. Albert C. J. Luo is a Distinguished Research Professor at the Department of Mechanical Engineering at Southern Illinois University Edwardsville, USA. He received his Ph.D. degree from the University of Manitoba, Canada, in 1995. His research focuses on mechanics, dynamics and mechanical vibration, and he has published over 40 books, and more than 200 journal articles and conference papers in these fields. He received the Paul Simon Outstanding Scholar Award in 2008 and an ASME fellowship in 2007. He now serves as Co-editor of the Journal of Applied Nonlinear Dynamics and Editor of various book series, including “Nonlinear Systems and Complexity,” and “Nonlinear Physical Science.”
Bibliographic Information
Book Title: Bifurcation and Stability in Nonlinear Discrete Systems
Authors: Albert C. J. Luo
Series Title: Nonlinear Physical Science
DOI: https://doi.org/10.1007/978-981-15-5212-0
Publisher: Springer Singapore
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Higher Education Press 2020
Hardcover ISBN: 978-981-15-5211-3Published: 14 August 2020
Softcover ISBN: 978-981-15-5214-4Published: 15 August 2021
eBook ISBN: 978-981-15-5212-0Published: 13 August 2020
Series ISSN: 1867-8440
Series E-ISSN: 1867-8459
Edition Number: 1
Number of Pages: X, 313
Number of Illustrations: 27 b/w illustrations, 16 illustrations in colour
Topics: Complexity, Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Control and Systems Theory