Bifurcation Dynamics in Polynomial Discrete Systems

✍ Scribed by Albert C. J. Luo

• Publisher: Springer Singapore;Springer
• Year: 2020
• Tongue: English
• Leaves: 440
• Series: Nonlinear Physical Science
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xi
Quadratic Nonlinear Discrete Systems (Albert C. J. Luo)....Pages 1-92
Cubic Nonlinear Discrete Systems (Albert C. J. Luo)....Pages 93-166
Quartic Nonlinear Discrete Systems (Albert C. J. Luo)....Pages 167-256
(2m)th-Degree Polynomial Discrete Systems (Albert C. J. Luo)....Pages 257-334
(2m + 1)th-Degree Polynomial Discrete Systems (Albert C. J. Luo)....Pages 335-428
Back Matter ....Pages 429-430

✦ Subjects

Engineering; Complexity; Dynamical Systems and Ergodic Theory; Vibration, Dynamical Systems, Control; Control