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A novel four-wing non-equilibrium chaotic system and its circuit implementation

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Abstract

In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilibria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps. There is little difference between this chaotic system without equilibria and other chaotic systems with equilibria shown by phase portraits and Lyapunov exponents. But the bifurcation diagram shows that the chaotic systems without equilibria do not have characteristics such as pitchfork bifurcation, Hopf bifurcation etc. which are common to the normal chaotic systems. The Poincaré maps show that this system is a four-wing chaotic system with more complicated dynamics. Moreover, the physical existence of the four-wing chaotic attractor without equilibria is verified by an electronic circuit.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 61274020) and the Open Fund Project of Key Laboratory in Hunan University (Grant No. 13K015).

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Authors and Affiliations

  1. College of Information Science and Engineering, Hunan University, Changsha, 410082, China

    YUAN LIN, CHUNHUA WANG, HAIZHEN HE & LI LI ZHOU

  2. College of Electrical and Information Engineering, Hunan Institute of Engineering, Xiangtan, 411104, China

    YUAN LIN

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  1. YUAN LIN
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  2. CHUNHUA WANG
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  3. HAIZHEN HE
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  4. LI LI ZHOU
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Correspondence to YUAN LIN.

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LIN, Y., WANG, C., HE, H. et al. A novel four-wing non-equilibrium chaotic system and its circuit implementation. Pramana - J Phys 86, 801–807 (2016). https://doi.org/10.1007/s12043-015-1118-1

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  • DOI: https://doi.org/10.1007/s12043-015-1118-1

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