Bifurcation and stability in nonlinear discrete systems. With 43 figures
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 Book is suitable for senior undergraduate and graduate students as well as practical engineers, scientist and researchers interested in bifurcation and stability of nonlinear systems.
scientific article; zbMATH DE number 7224520