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A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system

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Abstract

This paper presents a new four-dimensional (4-D) smooth quadratic autonomous chaotic system, which can present periodic orbit, chaos, and hyper-chaos under the conditions on different parameters. Importantly, the system can generate a four-wing hyper-chaotic attractor and a pair of coexistent double-wing hyper-chaotic attractors with two symmetrical initial conditions. Furthermore, a four-wing transient chaos occurs in the system. The dynamic analysis approach- in the paper involves time series, phase portraits, Poincaré maps, bifurcation diagrams, and Lyapunov exponents, to investigate some basic dynamical behaviors of the proposed 4-D system.

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Authors and Affiliations

  1. F’SATIE and Department of Electrical Engineering, Tshwane University of Technology, Pretoria, 0001, South Africa

    Shijian Cang & Guoyuan Qi

  2. Department of Industry Design, Tianjin University of Science and Technology, Tianjin, 300222, P.R. China

    Shijian Cang

  3. Department of Automation, Nankai University, Tianjin, 300071, P.R. China

    Zengqiang Chen

Authors
  1. Shijian Cang
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  2. Guoyuan Qi
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  3. Zengqiang Chen
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Correspondence to Shijian Cang.

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Cang, S., Qi, G. & Chen, Z. A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system. Nonlinear Dyn 59, 515–527 (2010). https://doi.org/10.1007/s11071-009-9558-0

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  • DOI: https://doi.org/10.1007/s11071-009-9558-0

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