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
  • [1] Al-Talib Z. S., 2020, Indonesian Journal of Electrical Engineering and Computer Science, V19, P715
  • [2] Switching of behavior: From hyperchaotic to controlled magnetoconvection model
    Ayub, Javeria
    Aqeel, Muhammad
    Abbasi, Javeria Nawaz
    Sunny, Danish Ali
    Rana, Zainab
    [J]. AIP ADVANCES, 2019, 9 (12)
  • [3] A secure communication method based on 6-D hyperchaos and circuit implementation
    Bian, YuYan
    Yu, WenXin
    [J]. TELECOMMUNICATION SYSTEMS, 2021, 77 (04) : 731 - 751
  • [4] Hopf bifurcation and chaos control in a new chaotic system via hybrid control strategy
    Cai, P.
    Yuan, Z. Z.
    [J]. CHINESE JOURNAL OF PHYSICS, 2017, 55 (01) : 64 - 70
  • [5] A new Lorenz-type hyperchaotic system with a curve of equilibria
    Chen, Yuming
    Yang, Qigui
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2015, 112 : 40 - 55
  • [6] Competitive modes and estimation of ultimate bound sets for a chaotic dynamical financial system
    Chien, Fengsheng
    Chowdhury, A. Roy
    Nik, Hassan Saberi
    [J]. NONLINEAR DYNAMICS, 2021, 106 (04) : 3601 - 3614
  • [7] A new 4D hyperchaotic system and its control
    Cui, Ning
    Li, Junhong
    [J]. AIMS MATHEMATICS, 2023, 8 (01): : 905 - 923
  • [8] Dynamics and Control of a Vibrating System with Hyperchaotic Behavior Using an Electronic Circuit Implementation
    Daum, Hilson H.
    Tusset, Angelo M.
    Ribeiro, Mauricio A.
    Balthazar, Jose M.
    Bueno, Atila M.
    Litak, Grzegorz
    [J]. BRAZILIAN JOURNAL OF PHYSICS, 2022, 52 (03)
  • [9] ROUTH-HURWITZ CRITERION IN THE EXAMINATION OF EIGENVALUES OF A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL-EQUATIONS
    DEJESUS, EX
    KAUFMAN, C
    [J]. PHYSICAL REVIEW A, 1987, 35 (12): : 5288 - 5290
  • [10] Retardational Effect and Hopf Bifurcations in a New Attitude System of Quad-Rotor Unmanned Aerial Vehicle
    Fiaz, Muhammad
    Aqeel, Muhammad
    Marwan, Muhammad
    Sabir, Muhammad
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (09):
123456