Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system |
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Authors: | Dong En-Zeng ab Chen Zeng-Qiang a Chen Zai-Ping b and Ni Jian-Yun |
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Affiliation: | b) a) Department of Automation,Nankai University,Tianjin 300071,China b) 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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