Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system |
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Authors: | Dong En-Zeng Chen Zeng-Qiang Chen Zai-Ping and Ni Jian-Yun |
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Institution: | Department of Automation, Nankai University, Tianjin 300071, China;Department of Automation, Tianjin University of Technology, Tianjin 300384, China;Department of Automation, Nankai University, Tianjin 300071, China;Department of Automation, Tianjin University of Technology, Tianjin 300384, China;Department of Automation, Tianjin University of Technology, Tianjin 300384, China |
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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. |
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Keywords: | hyper-chaos Chen system pitchfork bifurcation center manifold theorem |
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