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A novel simple no-equilibrium chaotic system with complex hidden dynamics

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Abstract

By utilizing a linear state feedback controller in the famous Sprott-S system, a novel no-equilibrium autonomous chaotic system is introduced in this paper. Although the newly proposed system is simple and elegant with eight terms including only one nonlinear term, it exhibits extremely rich and complex hidden dynamical behaviors such as hidden multistability and invariable Lyapunov exponents. Interestingly, the freedom of offset boosting of a variable is obtained by using a controlled constant. The complicated hidden dynamic characteristics of this no-equilibrium system are investigated by means of phase portraits, bifurcation diagrams, Lyapunov exponents, chaos diagram and so on. Furthermore, the corresponding implementation circuit is designed. The Multisim simulations and the hardware experimental results are in agreement with the numerical simulations of the same system on the Matlab platform, which verifies the feasibility of this new no-equilibrium system.

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Acknowledgements

The work was supported by the National Natural Science Foundations of China under Grant Nos. 61471310 and 61176032, and the Natural Science Foundations of Hunan Province, China under Grant No. 2015JJ2142.

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Authors and Affiliations

  1. School of Physics and Opotoelectric Engineering, Xiangtan University, Xiangtan, 411105, Hunan, China

    Sen Zhang & Yicheng Zeng

  2. College of Information Engineering, Xiangtan University, Xiangtan, 411105, Hunan, China

    Zhijun Li, Mengjiao Wang, Xu Zhang & De Chang

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  1. Sen Zhang
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  2. Yicheng Zeng
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  3. Zhijun Li
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Correspondence to Yicheng Zeng.

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Zhang, S., Zeng, Y., Li, Z. et al. A novel simple no-equilibrium chaotic system with complex hidden dynamics. Int. J. Dynam. Control 6, 1465–1476 (2018). https://doi.org/10.1007/s40435-018-0413-3

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