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
收藏
页码：1 / 29
页数：29
相关论文
共 50 条
  • [1] On bifurcations and local stability in 1-D nonlinear discrete dynamical systems
    Albert C. J. Luo
    International Journal of Dynamics and Control, 2021, 9 : 1 - 29
  • [2] Stability and Bifurcations Analysis of Discrete Dynamical Systems
    Khan, A. Q.
    Ibrahim, Tarek F.
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2019, 2019
  • [3] Stability for systems of 1-D coupled nonlinear oscillators
    Morosanu, Gheorghe
    Vladimirescu, Cristian
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 59
  • [4] A SIMPLIFIED STABILITY TEST FOR 1-D DISCRETE-SYSTEMS
    KAMAT, PS
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1986, 321 (04): : 193 - 201
  • [5] Local versus global stability in dynamical systems with consecutive Hopf bifurcations
    Böttcher P.C.
    Schäfer B.
    Kettemann S.
    Agert C.
    Witthaut D.
    Physical Review Research, 2023, 5 (03):
  • [6] Testing stability of 2-D discrete systems by a set of real 1-D stability tests
    Bistritz, Y
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2004, 51 (07): : 1312 - 1320
  • [7] On testing stability of 2-D discrete systems by a finite collection of 1-D stability tests
    Bistritz, Y
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2002, 49 (11): : 1634 - 1638
  • [8] Gap bifurcations in nonlinear dynamical systems
    Rizzato, FB
    Pakter, R
    PHYSICAL REVIEW LETTERS, 2002, 89 (18) : 1 - 184102
  • [9] Stability and Bifurcations in 2D Spatiotemporal Discrete Systems
    Sahari, Mohamed Lamine
    Taha, Abdel-Kaddous
    Randriamihamison, Louis
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, 28 (08):
  • [10] Representation of single neuron dynamics using 1-D and 2-D Discrete dynamical systems
    Zeki, Mustafa
    Kapcak, Sinan
    BIOMEDICAL PHYSICS & ENGINEERING EXPRESS, 2023, 9 (05)
12345