Two-dimensional Crossing and Product Polynomial Systems

Albert C. J. Luo (Autor)

Buch | Hardcover

440 Seiten

2026
Springer Nature Switzerland AG (Verlag)
978-981-96-5714-8 (ISBN)

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This book is about hybrid networks of singular and non-singular, one-dimensional flows and equilibriums in crossing and product polynomial systems. The singular equilibriums and one-dimensional flows with infinite-equilibriums in product polynomial systems are presented in the theorem. The singular equilibriums are singular saddles and centers, parabola-saddles, and double-inflection-saddles. The singular one-dimensional flows are singular hyperbolic-flows, hyperbolic-to-hyperbolic-secant flows, inflection-source and sink flows, and inflection-saddle flows. The higher-order singular one-dimensional flows and singular equilibriums are for the appearing bifurcations of lower-order singular and non-singular one-dimensional flows and equilibriums. The infinite-equilibriums are the switching bifurcations for two associated networks of singular and non-singular, one-dimensional flows and equilibriums. The corresponding mathematical conditions are presented, and the theory for nonlinear dynamics of crossing and product polynomial systems is presented through a theorem. The mathematical proof is completed through the local analysis and the first integral manifolds. The illustrations of singular one-dimensional flows and equilibriums are completed, and the sampled networks of non-singular one-dimensional flows and equilibriums are presented in this book.

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 Product Polynomial Systems.- Proof of Theorem.- Singular flows bifurcaions and networks.

Erscheinungsdatum	29.11.2025
Zusatzinfo	66 Illustrations, color; 1 Illustrations, black and white
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Crossing and Product Polynomial Systems • Hybrid networks of singular and regular equilibriums • Infinite-equilibriums and switching bifurcations • Inflection-sink, source and saddle flows • Parabola-saddles and double-inflection saddles • Singular hyperbolic and hyperbolic-secant flows • Singular saddle and center equilibriums
ISBN-10	981-96-5714-8 / 9819657148
ISBN-13	978-981-96-5714-8 / 9789819657148
Zustand	Neuware