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 50 条
  • [1] Hopf bifurcation analysis in a 4D-hyperchaotic system
    Kangming Zhang
    Qigui Yang
    Journal of Systems Science and Complexity, 2010, 23 : 748 - 758
  • [2] A new 4D hyperchaotic system and its control
    Cui, Ning
    Li, Junhong
    AIMS MATHEMATICS, 2023, 8 (01): : 905 - 923
  • [3] HOPF BIFURCATION ANALYSIS IN A 4D-HYPERCHAOTIC SYSTEM
    Kangming ZHANG School of Mathematical Sciences
    Department of Science and Arts
    JournalofSystemsScience&Complexity, 2010, 23 (04) : 748 - 758
  • [4] Hopf bifurcation analysis in a 4D-hyperchaotic system
    Zhang, Kangming
    Yang, Qigui
    JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2010, 23 (04) : 748 - 758
  • [5] Hopf Bifurcation Control of a Hyperchaotic Circuit System
    LIANG Cui-Xiang
    CommunicationsinTheoreticalPhysics, 2009, 52 (09) : 457 - 462
  • [6] Hopf Bifurcation Control of a Hyperchaotic Circuit System
    Liang Cui-Xiang
    Tang Jia-Shi
    Liu Su-Hua
    Han Feng
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2009, 52 (03) : 457 - 462
  • [7] HOPF BIFURCATION ANALYSIS AND AMPLITUDE CONTROL OF A NEW 4D HYPER-CHAOTIC SYSTEM
    Cai, Ping
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2018, (40): : 301 - 310
  • [8] Bifurcation and Periodic Solutions in Memristive Hyperchaotic System
    Zhong, Xiaoyun
    Peng, Minfang
    Shahidehpour, Mohammad
    Guo, Shangjiang
    IEEE ACCESS, 2018, 6 : 23202 - 23212
  • [9] Chaos control for a 4D hyperchaotic system
    Xu Changjin
    Li Peiluan
    APPLIED MECHATRONICS AND ANDROID ROBOTICS, 2013, 418 : 84 - +
  • [10] Anti-control of Hopf bifurcation at zero equilibrium of 4D Qi system
    Liu Su-Hua
    Tang Jia-Shi
    ACTA PHYSICA SINICA, 2008, 57 (10) : 6162 - 6168
12345