Bifurcation and stability in nonlinear discrete systems. With 43 figures
type: Item
instance of: scholarly article
title: Bifurcation and stability in nonlinear discrete systems. With 43 figures
DOI: 10.1007/978-981-15-5212-0
author: Albert C. J. Luo
published in: Nonlinear Physical Science
publication date: 2020-07-24T00:00:00Z
review text: This book is organized as follows with five chapters: 1 Local Stability and Bifurcations Discrete Systems; Fixed-Points and Stability; Stability Switching; Monotonic and Oscillatory Stability; Spiral Stability; Local Bifurcations; Monotonic Bifurcations; One-Step Oscillatory Bifurcations; Two-Step Oscillatory Bifurcations; Neimark Bifurcations; and References 2 Low-Dimensional Discrete Systems One-Dimensional Discrete Systems; Monotonic and Oscillatory Stability; Bifurcations; Monotonic Bifurcations; One-Step Oscillatory Bifurcations; Two-Step Oscillatory Bifurcations; Sample Bifurcation Analysis; Saddle-Node Appearing Bifurcation; Saddle-Node Switching Bifurcations; Third-Order Monotonic Sink Pitchfork Bifurcations; Third-Order Monotonic Source Pitchfork Bifurcations; Two-Dimensional Discrete Systems; Stability and Singularity; An Example; and References 3 Global Stability of 1-D Discrete Systems Discrete System Classifications, Fixed-Point Global Stability; One Fixed-Point Systems; Monotonic Stability; Oscillatory Stability; Two-Fixed-Point Systems; Monotonic Two-Fixed-Point Systems; Oscillatory Two-Fixed-Point Systems; Three-Fixed-Point Systems; Monotonic Three-Fixed-Point Systems;Oscillatory Three-Fixed-Point Systems; and References 4 Forward and Backward Discrete Systems Yin-Yang Theory of Discrete Systems; Forward Discrete Systems; Backward Discrete Systems; and Reference 5 Infinite-Fixed-Point Discrete Systems Fixed-Point Computations;Normal Forms of Discrete Systems; Infinite-Fixed-Point Systems; One-Infinite-Fixed-Point Systems; Two-Infinite-Fixed-Point Systems; Higher-Order Infinite-Fixed-Point Systems; Infinite-Fixed-Point-Network Systems; An Infinite-Fixed-Point-Network System; A Spiral Infinite-Fixed-Point System; A Linear Infinite-Fixed-Point System; A Hyperbolic Infinite-Fixed-Point System; and References In addition it has Index. The book is well organized and presents the most important notions of bifurcation and stability of nonlinear systems. The …
reviewed by: Seenith Sivasundaram
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D23
zbMATH DE Number: 7224520
zbMATH Keywords: bifurcation
zbMATH Keywords: stability
zbMATH Keywords: nonlinear discerete systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-981-15-5212-0
OpenAlex ID: W3048407961
description: scientific article; zbMATH DE number 7224520