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Bifurcations of invariant torus and knotted periodic orbits for the generalized Hopf–Langford system

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Abstract

In this paper, we study the bifurcations of invariant torus and knotted periodic orbits for the generalized Hopf-Langford system. By using bifurcation theory of dynamical systems, we obtain the exact explicit form of the heteroclinic orbits and knot periodic orbits. Moreover, under small perturbation, we prove that the perturbed planar system has two symmetric stable limit cycles created by Poincare bifurcations. Therefore, the corresponding three-dimensional perturbed system has an attractive invariant rotation torus.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This research was jointly supported by the National Natural Science Foundation of China under Grant (Nos. 11871231, 12071162, 11701191, 11401229).

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, Fujian, People’s Republic of China

    Yanggeng Fu & Jibin Li

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejing, People’s Republic of China

    Jibin Li

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  1. Yanggeng Fu
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  2. Jibin Li
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Correspondence to Jibin Li.

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Fu, Y., Li, J. Bifurcations of invariant torus and knotted periodic orbits for the generalized Hopf–Langford system. Nonlinear Dyn 106, 2097–2105 (2021). https://doi.org/10.1007/s11071-021-06839-9

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