Bifurcation Dynamics in Polynomial Discrete Systems
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Beschreibung
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.
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.
Is the first book focusing on bifurcation dynamics in 1-dimensional polynomial nonlinear discrete systems Discusses appearing and switching bifurcations for simple and higher-order singularity period-1 fixed-points in 1-dimensional polynomial discrete systems Provides a new methodology for singularity analysis in nonlinear discrete systems, such as big data analysis and data-driving dynamical system analysis
Autor*in
Albert C. J. Luo
Themen in »Bifurcation Dynamics in Polynomial Discrete Systems«
Bifurcation dynamics Polynomial nonlinear discrete systems Period-doubling renormalization Period-n appearing and period-doublization Appearing and switching bifurcations
Stimmen zu »Bifurcation Dynamics in Polynomial Discrete Systems«
“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)
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