1-dimensional Flow Arrays and Bifurcations in Planar Polynomial Systems

Albert C. J. Luo (Autor)

Buch | Hardcover

377 Seiten

2024 | 2024 ed.
Springer Verlag, Singapore
978-981-97-2203-7 (ISBN)

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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.

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”.

Constant and Self variable Polynomial Systems.- Constant and Crossing variable Polynomial Systems.- Single univariate Polynomial Systems.- Higher order Infinite equilibrium Bifurcations.

Erscheinungsdatum	14.12.2024
Zusatzinfo	48 Illustrations, color; 1 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	1-dimensional flow arrays • Infinite-equilibriums and switching bifurcations • Parabola and inflection flows • Sink, source and saddle flows • Two-dimensional polynomial systems
ISBN-10	981-97-2203-9 / 9819722039
ISBN-13	978-981-97-2203-7 / 9789819722037
Zustand	Neuware