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

被引：4
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, DOI 10.11591/ijeecs.v19.i2.pp715-722
[2]   Switching of behavior: From hyperchaotic to controlled magnetoconvection model [J].
Ayub, Javeria ;
Aqeel, Muhammad ;
Abbasi, Javeria Nawaz ;
Sunny, Danish Ali ;
Rana, Zainab .
AIP ADVANCES, 2019, 9 (12)
[3]   A secure communication method based on 6-D hyperchaos and circuit implementation [J].
Bian, YuYan ;
Yu, WenXin .
TELECOMMUNICATION SYSTEMS, 2021, 77 (04) :731-751
[4]   Hopf bifurcation and chaos control in a new chaotic system via hybrid control strategy [J].
Cai, P. ;
Yuan, Z. Z. .
CHINESE JOURNAL OF PHYSICS, 2017, 55 (01) :64-70
[5]   A new Lorenz-type hyperchaotic system with a curve of equilibria [J].
Chen, Yuming ;
Yang, Qigui .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2015, 112 :40-55
[6]   Competitive modes and estimation of ultimate bound sets for a chaotic dynamical financial system [J].
Chien, Fengsheng ;
Chowdhury, A. Roy ;
Nik, Hassan Saberi .
NONLINEAR DYNAMICS, 2021, 106 (04) :3601-3614
[7]   A new 4D hyperchaotic system and its control [J].
Cui, Ning ;
Li, Junhong .
AIMS MATHEMATICS, 2023, 8 (01) :905-923
[8]   Dynamics and Control of a Vibrating System with Hyperchaotic Behavior Using an Electronic Circuit Implementation [J].
Daum, Hilson H. ;
Tusset, Angelo M. ;
Ribeiro, Mauricio A. ;
Balthazar, Jose M. ;
Bueno, Atila M. ;
Litak, Grzegorz .
BRAZILIAN JOURNAL OF PHYSICS, 2022, 52 (03)
[9]   ROUTH-HURWITZ CRITERION IN THE EXAMINATION OF EIGENVALUES OF A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL-EQUATIONS [J].
DEJESUS, EX ;
KAUFMAN, C .
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 [J].
Fiaz, Muhammad ;
Aqeel, Muhammad ;
Marwan, Muhammad ;
Sabir, Muhammad .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (09)
123456