Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System

被引：3
作者：
Liu, Yu [1 ]
Zhou, Yan [1 ,2 ]
Guo, Biyao [1 ]
机构：
[1] Inner Mongolia Normal Univ, Coll Math Sci, Hohhot 010022, Peoples R China
[2] Inner Mongolia Normal Univ, Ctr Appl Math Sci, Hohhot 010022, Peoples R China
来源：
MATHEMATICS | 2023年 / 11卷 / 12期
基金：
中国国家自然科学基金;
关键词：
hyperchaotic system; Hopf bifurcation; periodic solutions; hyperchaos control; normal form theory; CHAOTIC SYSTEM; SYNCHRONIZATION; CIRCUIT;
D O I：
10.3390/math11122699
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a new four-dimensional (4D) hyperchaotic biplane system is designed and presented. The dynamical properties of this new system are studied by means of tools such as bifurcation diagrams, Lyapunov exponents and phase diagrams. The Hopf bifurcation and periodic solutions of this hyperchaotic system are solved analytically. In addition, a new hyperchaotic control strategy is applied, and a comparative analysis of the controlled system is performed.
引用
收藏
页数：14
相关论文
共 52 条
  • [31] Hyperchaos and Multistability in a Four-Dimensional Financial Mathematical Model
    Rech, Paulo C.
    [J]. JOURNAL OF APPLIED NONLINEAR DYNAMICS, 2021, 10 (02) : 211 - 218
  • [32] EQUATION FOR HYPERCHAOS
    ROSSLER, OE
    [J]. PHYSICS LETTERS A, 1979, 71 (2-3) : 155 - 157
  • [33] Hidden attractors in a new complex generalised Lorenz hyperchaotic system, its synchronisation using adaptive contraction theory, circuit validation and application
    Singh, Jay Prakash
    Roy, B. K.
    [J]. NONLINEAR DYNAMICS, 2018, 92 (02) : 373 - 394
  • [34] SOME SIMPLE CHAOTIC FLOWS
    SPROTT, JC
    [J]. PHYSICAL REVIEW E, 1994, 50 (02): : R647 - R650
  • [35] Vaidyanathan S., 2021, BACKSTEPPING CONTROL, P115, DOI [10.1016/B978-0-12-817582-8.00013-1, DOI 10.1016/B978-0-12-817582-8.00013-1]
  • [36] Vaidyanathan S., 2015, J ENG SCI TECHNOLOGY, V8, P232, DOI [10.25103/jestr.082.29, DOI 10.25103/JESTR.082.29]
  • [37] A new multistable double-scroll 4-D hyperchaotic system with no equilibrium point, its bifurcation analysis, synchronization and circuit design
    Vaidyanathan, Sundarapandian
    He, Shaobo
    Sambas, Aceng
    [J]. ARCHIVES OF CONTROL SCIENCES, 2021, 31 (01) : 99 - 128
  • [38] A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation
    Vaidyanathan, Sundarapandian
    Azar, Ahmad Taher
    Boulkroune, Abdesselem
    [J]. INTERNATIONAL JOURNAL OF AUTOMATION AND CONTROL, 2018, 12 (01) : 5 - 26
  • [39] BIFURCATIONS, ULTIMATE BOUNDEDNESS AND SINGULAR ORBITS IN A UNIFIED HYPERCHAOTIC LORENZ-TYPE SYSTEM
    Wang, Haijun
    Zhang, Fumin
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (05): : 1791 - 1820
  • [40] Melnikov-type method for a class of planar hybrid piecewise-smooth systems with impulsive effect and noise excitation: Heteroclinic orbits
    Wei, Zhouchao
    Li, Yuxi
    Moroz, Irene
    Zhang, Wei
    [J]. CHAOS, 2022, 32 (10)
123456