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
  • [31] On Some Discrete Nonlinear Dynamical Systems
    Sekovanov V.S.
    Sekovanov V.S.
    Journal of Mathematical Sciences, 2019, 237 (3) : 460 - 472
  • [32] Discrete Holomorphic Local Dynamical Systems
    Abate, Marco
    HOLOMORPHIC DYNAMICAL SYSTEMS, 2010, 1998 : 1 - 55
  • [33] On Local Asymptotic Stability of q-Fractional Nonlinear Dynamical Systems
    Koca, Ilknur
    Demirci, Elif
    APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, 2016, 11 (01): : 174 - 183
  • [34] 1-D Schrodinger operators with local point interactions on a discrete set
    Kostenko, Aleksey S.
    Malamud, Mark M.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (02) : 253 - 304
  • [35] On the stability for a class of discrete dynamical systems
    Feng, BL
    Yu, YH
    3RD INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS, 1998, : 789 - 793
  • [36] Global stability of discrete dynamical systems
    Jin, MZ
    Ying, D
    Li, CX
    PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS, 2002, : 1220 - 1223
  • [37] Toward a Comprehensive Theory for Stability Regions of a Class of Nonlinear Discrete Dynamical Systems
    Dias, Elaine Santos
    Costa Alberto, Luis Fernando
    Amaral, Fabiolo Moraes
    Chiang, Hsiao-Dong
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2021, 66 (09) : 4371 - 4377
  • [38] Coherence resonance at noisy precursors of bifurcations in nonlinear dynamical systems
    Neiman, A
    Saparin, PI
    Stone, L
    PHYSICAL REVIEW E, 1997, 56 (01): : 270 - 273
  • [39] A reflection on nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    Virgin, L. N.
    JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2006, 1 (04): : 277 - 278
  • [40] HIGHER DIMENSIONAL TOPOLOGY AND GENERALIZED HOPF BIFURCATIONS FOR DISCRETE DYNAMICAL SYSTEMS
    Barge, Hector
    Sanjurjo, Jose M. R.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2022, 42 (06) : 2585 - 2601
12345