Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

doi:10.1088/1674-1056/21/3/030501

中国物理B ›› 2012, Vol. 21 ›› Issue (3): 30501-030501.doi: 10.1088/1674-1056/21/3/030501

董恩增¹ ²,陈增强¹,陈在平²,倪建云²

收稿日期:2011-10-06 修回日期:2011-10-19 出版日期:2012-02-15 发布日期:2012-02-15
通讯作者: 董恩增,dongenzeng@163.com E-mail:dongenzeng@163.com

Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

Dong En-Zeng(董恩增)^a)b)^†, Chen Zeng-Qiang(陈增强)^a), Chen Zai-Ping(陈在平)^b), and Ni Jian-Yun(倪建云)^b)

a. Department of Automation, Nankai University, Tianjin 300071, China;
b. Department of Automation, Tianjin University of Technology, Tianjin 300384, China

Received:2011-10-06 Revised:2011-10-19 Online:2012-02-15 Published:2012-02-15
Contact: Dong En-Zeng,dongenzeng@163.com E-mail:dongenzeng@163.com
Supported by:
Project supported by the Natural Science Foundation of China (Grant Nos. 61174094, 50977063, and 60904063), the Foundation of the Application Base and Frontier Technology Research Project of Tianjin, China (Grant No. 10JCZDJC23100), the Development of Science and Technology Foundation of the Higher Education Institutions of Tianjin, China (Grant No. 20080826).

摘要/Abstract

Abstract: In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic attractor in wide parameters regions. By using the center manifold theorem and the local bifurcation theory, a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point. Numerical analysis demonstrates that the hyper-chaotic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-chaotic system is useful in the secure communication.

Key words: hyper-chaos, Chen system, pitchfork bifurcation, center manifold theorem

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)

董恩增, 陈增强, 陈在平, 倪建云. [J]. 中国物理B, 2012, 21(3): 30501-030501.

Dong En-Zeng(董恩增), Chen Zeng-Qiang(陈增强), Chen Zai-Ping(陈在平), and Ni Jian-Yun(倪建云) . Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system[J]. Chin. Phys. B, 2012, 21(3): 30501-030501.

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Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

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