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Jacobi Stability Analysis of Liu System: Detecting Chaos

Author

Listed:
  • Qinghui Liu

    (College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, China)

  • Xin Zhang

    (School of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing 210023, China)

Abstract

By utilizing the Kosambi–Cartan–Chern (KCC) geometric theory, this paper is dedicated to providing novel insights into the Liu dynamical system, which stands out as one of the most distinctive and noteworthy nonlinear dynamical systems. Firstly, five important geometrical invariants of the system are obtained by associating the nonlinear connection with the Berwald connection. Secondly, in terms of the eigenvalues of the deviation curvature tensor, the Jacobi stability of the Liu dynamical system at fixed points is investigated, which indicates that three fixed points are Jacobi unstable. The Jacobi stability of the system is analyzed and compared with that of Lyapunov stability. Lastly, the dynamical behavior of components of the deviation vector is studied, which serves to geometrically delineate the chaotic behavior of the system near the origin. The onset of chaos for the Liu dynamical system is obtained. This work provides an analysis of the Jacobi stability of the Liu dynamical system, serving as a useful reference for future chaotic system research.

Suggested Citation

  • Qinghui Liu & Xin Zhang, 2024. "Jacobi Stability Analysis of Liu System: Detecting Chaos," Mathematics, MDPI, vol. 12(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1981-:d:1422980
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    References listed on IDEAS

    as
    1. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
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