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A new hyperchaotic system with Hopf bifurcation and its boundedness: infinite coexisting hidden and self-excited attractor

  • Mathematical methods in data science
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Abstract

This paper investigates the dynamical innovations occur in an upgraded chaotic Pan system. The local dynamics includes the stability analysis, types of attractor and Hopf bifurcation analysis. The proposed system undergoes periodic, chaotic and hyperchaotic orbits with the variation of bifurcation and control parameter. The hidden self-excited chaotic attractors are localized within the parametric boundaries; also, proposed system is initialized in the self-excited attractor zone where all the unstable equilibria exist. The hidden and self-existing attractor of hyperchaotic Pan system is revealed with the help of multidimensional transient dynamical system. Moreover, a complete set of conditions are derived that guarantee the existence of supercritical Hopf bifurcation in the upgraded chaotic Pan system. The Hopf bifurcation diagram is also investigated for numerical confirmation of analytical results.

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Data availability

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

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Authors and Affiliations

  1. Institute of Space Technology, Islamabad, Pakistan

    Javeria Ayub, Muhammad Aqeel & Danish Ali Sunny

Authors
  1. Javeria Ayub
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  2. Muhammad Aqeel
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  3. Danish Ali Sunny
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Contributions

JA and MA contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript. DA Sunny provided critical feedback and helped shape the research, analysis and manuscript.

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Correspondence to Javeria Ayub.

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Ayub, J., Aqeel, M. & Sunny, D.A. A new hyperchaotic system with Hopf bifurcation and its boundedness: infinite coexisting hidden and self-excited attractor. Soft Comput 27, 887–901 (2023). https://doi.org/10.1007/s00500-022-07608-5

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