On bifurcations and local stability in 1-D nonlinear discrete dynamical systems

被引：0

作者：

Luo, Albert C. J. ^{[1
]}

机构：

[1] Southern Illinois Univ Edwardsville, Dept Mech & Ind Engn, Edwardsville, IL 62026 USA

来源：

INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL | 2021年 / 9卷 / 01期

关键词：

Bifurcation; Stability; Fixed points; Saddle-node bifurcations; Sink bifurcations; Source bifurcations; ANALYTIC THEORY; DIFFERENCE; ORBITS;

D O I：

10.1007/s40435-020-00632-z

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, a theory of bifurcations and local stability of fixed-points (or period-1 solutions) in one-dimensional nonlinear discrete dynamical systems is presented. The linearized discrete dynamical systems are discussed first, and the higher-order singularity and monotonic and oscillatory stability of fixed-points for one-dimensional nonlinear discrete dynamical systems are presented. The monotonic and oscillatory bifurcations of fixed-points (period-1 solutions) are presented. A few special examples in 1-dimensional maps are presented for a better understanding of the general theory for the stability and bifurcation of nonlinear discrete dynamical systems. Global analysis of period-2 motions for the sampled nonlinear discrete dynamical systems are carried out, and global illustrations of period-1 to period-2 solutions in the sampled nonlinear discrete dynamical systems are given.

引用

页码：1 / 29

页数：29

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