Bifurcation and Stability in Nonlinear Discrete Systems

✍ Scribed by Albert C. J. Luo

• Publisher: Springer Singapore;Springer
• Year: 2020
• Tongue: English
• Leaves: 320
• Series: Nonlinear Physical Science
• Edition: 1st ed.
• Category: Library

✦ Synopsis

This book focuses on bifurcation and stability in nonlinear discrete systems, including monotonic and oscillatory stability. It presents the local monotonic and oscillatory stability and bifurcation of period-1 fixed-points on a specific eigenvector direction, and discusses the corresponding higher-order singularity of fixed-points. Further, it explores the global analysis of monotonic and oscillatory stability of fixed-points in 1-dimensional discrete systems through 1-dimensional polynomial discrete systems. Based on the Yin-Yang theory of nonlinear discrete systems, the book also addresses the dynamics of forward and backward nonlinear discrete systems, and the existence conditions of fixed-points in said systems. Lastly, in the context of local analysis, it describes the normal forms of nonlinear discrete systems and infinite-fixed-point discrete systems. Examining nonlinear discrete systems from various perspectives, the book helps readers gain a better understanding of the nonlinear dynamics of such systems.

✦ Table of Contents

Front Matter ....Pages i-x
Local Stability and Bifurcations (Albert C. J. Luo)....Pages 1-76
Low-Dimensional Discrete Systems (Albert C. J. Luo)....Pages 77-170
Global Stability of 1-D Discrete Systems (Albert C. J. Luo)....Pages 171-206
Forward and Backward Discrete Systems (Albert C. J. Luo)....Pages 207-249
Infinite-Fixed-Point Discrete Systems (Albert C. J. Luo)....Pages 251-309
Back Matter ....Pages 311-313

✦ Subjects

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