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Complex bursting patterns and their bifurcation mechanisms in the Φ6-van der Pol system with external and parametric excitations

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Abstract

Complex bursting patterns and the bifurcation generation mechanism are investigated in the parametrically and externally driven Φ6-van der Pol system. Five different bursting types, i.e. symmetric ‘subHopf\(\slash\)homoclinic’ bursting, symmetric ‘subHopf\(\slash\)fold-cycle’ bursting via ‘subHopf\(\slash\)subHopf’ hysteresis loop, symmetric ‘subHopf\(\slash\)fold-cycle’ bursting, ‘subHopf\(\slash\)subHopf’ bursting and ‘fold\(\slash\)fold’ bursting, are explored. First, the mechanism of symmetric ‘subHopf\(\slash\)fold-cycle’ bursting via ‘subHopf\(\slash\)subHopf’ hysteresis loop is revealed. Then, based on the two-parameter bifurcation analysis, dynamical evolutions of the symmetric bursting are presented. Different clusters appear when the parameter changes, leading to different patterns of bursting oscillations. In addition, we find that the jumping phenomenon depends not only on the fold bifurcation, but also on the subcritical Hopf bifurcation. Finally, numerical simulations are presented to demonstrate the correctness of the research.

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (Grant No. 11872188).

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Authors and Affiliations

  1. School of Mechanical Engineering, Nantong Institute of Technology, Nantong, 226002, People’s Republic of China

    Zhangyao Chen

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  1. Zhangyao Chen
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Correspondence to Zhangyao Chen.

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Chen, Z. Complex bursting patterns and their bifurcation mechanisms in the Φ6-van der Pol system with external and parametric excitations. Pramana - J Phys 96, 157 (2022). https://doi.org/10.1007/s12043-022-02402-2

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  • DOI: https://doi.org/10.1007/s12043-022-02402-2

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