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Bifurcation Dynamics in Polynomial Discrete Systems de Albert C. J. Luo

Bifurcation Dynamics in Polynomial Discrete Systems: Nonlinear Physical Science

Autor Albert C. J. Luo
en Limba Engleză Hardback – 10 noi 2020
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. 

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Specificații

ISBN-13: 9789811552076
ISBN-10: 981155207X
Pagini: 444
Ilustrații: XI, 430 p. 68 illus., 66 illus. in color.
Dimensiuni: 160 x 241 x 30 mm
Greutate: 0.78 kg
Ediția:1st edition 2020
Editura: Springer
Colecția Nonlinear Physical Science
Seria Nonlinear Physical Science

Locul publicării:Singapore, Singapore

Cuprins

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. 

Recenzii

“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)

Notă biografică

This book is a monograph about 1-dimensional flow arrays and bifurcations in constant and product polynomial systems. The 1-dimensional flows and the corresponding bifurcation dynamics are discussed. The singular hyperbolic and hyperbolic-secant flows are presented, and the singular hyperbolic-to-hyperbolic-secant flows are discussed. The singular inflection source, sink and upper, and lower-saddle flows are presented. The corresponding appearing and switching bifurcations are presented for the hyperbolic and hyperbolic-secant networks, and singular flows networks. The corresponding theorem is presented, and the proof of theorem is given. Based on the singular flows, the corresponding hyperbolic and hyperbolic-secant flows are illustrated for a better understanding of the dynamics of constant and product polynomial systems.

Textul de pe ultima copertă

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.

Caracteristici

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