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
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.
Fund: 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).
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 2012 Chin. Phys. B 21 030501
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