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A New Five-Dimensional Hyperchaotic System with Six Coexisting Attractors

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Abstract

This article presents a hyperchaotic system of five-dimensional autonomous ODEs that has five cross-product nonlinearities. Under certain parametric conditions, it exhibits three different types of hyperchaotic and chaotic systems which correspond to six hyperchaotic attractors with a non-hyperbolic equilibrium line, four chaotic attractors with seventeen hyperbolic equilibria, and four chaotic attractors with only one hyperbolic equilibrium, respectively. The fundamental dynamics are analyzed theoretically and numerically, such as the onset of hyperchaos and chaos, routes to chaos, persistence of chaos, coexistence of attractors, periodic windows and bifurcations. It is particularly shown that the coexisting attractors of the 5D system inside the hypercone are symmetric. Some dynamical characteristics of these attractors are illustrated.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

Jiaopeng Yang is supported by the Overseas Short-term Study Program of SCUT. Zhengrong Liu is supported by NSF of China (Nos. 11971176 and 11771152), and Fundamental Research Foundation for the Central Universities (2019MS111).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006, China

    Jiaopeng Yang

  2. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, 78539, USA

    Jiaopeng Yang & Zhaosheng Feng

  3. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Zhengrong Liu

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  1. Jiaopeng Yang
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  2. Zhaosheng Feng
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Correspondence to Zhaosheng Feng.

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Yang, J., Feng, Z. & Liu, Z. A New Five-Dimensional Hyperchaotic System with Six Coexisting Attractors. Qual. Theory Dyn. Syst. 20, 18 (2021). https://doi.org/10.1007/s12346-021-00454-0

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  • DOI: https://doi.org/10.1007/s12346-021-00454-0

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