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.
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页码：1 / 29
页数：29
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