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Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system

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Abstract

This paper analyzes the hyperchaotic behaviors of the newly presented simplified Lorenz system by using a sinusoidal parameter variation and hyperchaos control of the forced system via feedback. Through dynamic simulations which include phase portraits, Lyapunov exponents, bifurcation diagrams, and Poincaré sections, we find the sinusoidal forcing not only suppresses chaotic behaviors, but also generates hyperchaos. The forced system also exhibits some typical bifurcations such as the pitchfork, period-doubling, and tangent bifurcations. Interestingly, three-attractor coexisting phenomenon happens at some specific parameter values. Furthermore, a feedback controller is designed for stabilizing the hyperchaos to periodic orbits, which is useful for engineering applications.

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Acknowledgements

This work was supported by the National Nature Science Foundation of People’s Republic of China (Grant No. 61161006), and the National Science Foundation for Post-doctoral Scientists of People’s Republic of China (Grant No. 20070420774). One of us (Xuan Liu) wishes to thank Prof. Guanrong Chen for discussions by E-mail.

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Authors and Affiliations

  1. School of Physics Science and Technology, Central South University, Changsha, 410083, P.R. China

    Keihui Sun, Xuan Liu & Congxu Zhu

  2. Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA

    J. C. Sprott

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  1. Keihui Sun
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  2. Xuan Liu
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  3. Congxu Zhu
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  4. J. C. Sprott
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Correspondence to Xuan Liu.

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Sun, K., Liu, X., Zhu, C. et al. Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system. Nonlinear Dyn 69, 1383–1391 (2012). https://doi.org/10.1007/s11071-012-0354-x

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  • DOI: https://doi.org/10.1007/s11071-012-0354-x

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