Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

doi:10.1088/1674-1056/22/8/080504

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80504-080504.doi: 10.1088/1674-1056/22/8/080504

Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

薛薇^a, 齐国元^b, 沐晶晶^a, 贾红艳^a, 郭彦岭^b

a Department of Automation, Tianjin University of Science & Technology, Tianjin 300222, China;
b F'SATI/Department of Electrical Engineering, Tshwane University of Technology, Pretoria 0001, South Africa

收稿日期:2012-11-12 修回日期:2013-01-16 出版日期:2013-06-27 发布日期:2013-06-27
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10772135 and 60874028), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11202148), the Incentive Funding of the National Research Foundation of South Africa (Grant No. IFR2009090800049), the Eskom Tertiary Education Support Programme of South Africa, and the Research Foundation of Tianjin University of Science and Technology.

Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

Xue Wei (薛薇)^a, Qi Guo-Yuan (齐国元)^b, Mu Jing-Jing (沐晶晶)^a, Jia Hong-Yan (贾红艳)^a, Guo Yan-Ling (郭彦岭)^b

a Department of Automation, Tianjin University of Science & Technology, Tianjin 300222, China;
b F'SATI/Department of Electrical Engineering, Tshwane University of Technology, Pretoria 0001, South Africa

Received:2012-11-12 Revised:2013-01-16 Online:2013-06-27 Published:2013-06-27
Contact: Xue Wei, Qi Guo-Yuan, Jia Hong-Yan E-mail:xuewei@tust.edu.cn; qig@tut.ac.za; jiahy@tust.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10772135 and 60874028), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11202148), the Incentive Funding of the National Research Foundation of South Africa (Grant No. IFR2009090800049), the Eskom Tertiary Education Support Programme of South Africa, and the Research Foundation of Tianjin University of Science and Technology.

摘要/Abstract

摘要： In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincaré maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.

关键词: hyper-chaos, four-wing chaotic system, one equilibrium, Hopf bifurcation, circuit implementation

Abstract: In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincaré maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.

Key words: hyper-chaos, four-wing chaotic system, one equilibrium, Hopf bifurcation, circuit implementation

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Pq (Numerical simulations of chaotic systems)

薛薇, 齐国元, 沐晶晶, 贾红艳, 郭彦岭. Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system[J]. 中国物理B, 2013, 22(8): 80504-080504.

Xue Wei (薛薇), Qi Guo-Yuan (齐国元), Mu Jing-Jing (沐晶晶), Jia Hong-Yan (贾红艳), Guo Yan-Ling (郭彦岭). Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system[J]. Chin. Phys. B, 2013, 22(8): 80504-080504.

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Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

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