This is the first book focusing on bifurcation dynamics in 1-dimensional polynomial nonlinear discrete systems. It comprehensively discusses the general mathematical conditions of bifurcations in polynomial nonlinear discrete systems, as well as appearing and switching bifurcations for simple and higher-order singularity period-1 fixed-points in the 1-dimensional polynomial discrete systems. Further, it analyzes the bifurcation trees of period-1 to chaos generated by period-doubling, and monotonic saddle-node bifurcations. Lastly, the book presents methods for period-2 and period-doubling renormalization for polynomial discrete systems, and describes the appearing mechanism and period-doublization of period-n fixed-points on bifurcation trees for the first time, offering readers fascinating insights into recent research results in nonlinear discrete systems.

Autorentext

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."

Zusammenfassung
"The author carried out a very detailed study of stability conditions and bifurcations and, in fact, opened a new direction of research in nonlinear dynamics. ... The book is of great interest for specialists working with polynomial discrete systems." (Anatoly Martynyuk, zbMATH 1467.93004, 2021)

Inhalt
Quadratic Nonlinear Discrete Systems.- Cubic Nonlinear Discrete Systems.- Quartic Nonlinear Discrete Systems.- (2m)th-degree Polynomial Discrete Systems.- (2m+1)th-degree polynomial discrete systems.- Subject index.