Overview
- Provides a reference work for students and researchers about dynamical systems and control
- Discusses 1-dimensional source, sink, and saddle flows as well as parabola and inflection flows
- Covers higher-order infinite-equilibriums and bifurcations
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Keywords
- Two-dimensional polynomial systems
- 1-dimensional flow arrays
- Sink, source and saddle flows
- Parabola and inflection flows
- Infinite-equilibriums and switching bifurcations
About this book
This book introduces to 1-dimensional flow arrays and bifurcations in planar polynomial systems. The 1-dimensional source, sink and saddle flows are discussed, as well as the 1-dimensional parabola and inflection flows. The singular source, sink and saddle flows are the appearing and switching bifurcations for simple sink and source flow arrays and for lower-order singular source, sink and saddle flow arrays. The singular parabola and inflection flows are the appearing and switching bifurcations for simple parabola arrays and also for lower-order singular parabola and inflection flow arrays. The infinite-equilibriums in single-variable polynomial systems are also discussed, which are the appearing and switching bifurcations of hybrid arrays of source, sink, and saddle flows with parabola and inflections. This book helps readers understand the global dynamics of planar polynomial systems and the Hilbert sixteen problem.
Authors and Affiliations
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 nonlinear dynamics, nonlinear mechanics, and nonlinear differential equations. He has published over 50 monographs, 20 edited books and more than 400 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 was an editor for Communications in Nonlinear Science and Numerical Simulation for 14 years, and an associate editor for ASME Journal of Computational and Nonlinear Dynamics, and International Journal of Bifurcation and Chaos. He now serves as a 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: 1-dimensional Flow Arrays and Bifurcations in Planar Polynomial Systems
Authors: Albert C. J. Luo
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Higher Education Press Limited Company 2024
Hardcover ISBN: 978-981-97-2203-7Due: 22 July 2024
Softcover ISBN: 978-981-97-2206-8Due: 22 July 2024
eBook ISBN: 978-981-97-2204-4Due: 22 July 2024
Edition Number: 1
Number of Pages: VII, 361
Number of Illustrations: 34 illustrations in colour