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Complex bursting dynamics in a Rayleigh–Liénard oscillator

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Abstract

In this paper, the intricate bursting oscillations in a Rayleigh–Liénard oscillator induced by parametric and external slow-varying excitations are proposed. By treating the slow-varying excitations as the generalized state variables, an autonomous system is produced. We identify symmetric bursting oscillations of four distinct types. By simultaneously overlapping the equilibrium branches and the transformed phase portraits and using the fast-slow analysis method, the generation principles of four bursting patterns are disclosed. To explore the parameter qualities associated with the existence of the heteroclinic and homoclinic bifurcations, the Melnikov method is utilized. In addition, we describe the Hopf delay generation mechanism and how the asymptotic theory is used to figure out the delay interval. Furthermore, the precision of the results is demonstrated using the numerical simulations.

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Data Availability Statement

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

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Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through Grant No. 12172333 and the Natural Science Foundation of Zhejiang through Grant No. LY20A020003. The authors gratefully acknowledge the reviewers for thoroughly examining our manuscripts and providing useful comments to guide our revision.

Funding

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (NNSFC) through Grant No. 12172333 and the Natural Science Foundation of Zhejiang through Grant No. LY20A020003.

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  1. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Haolan Wang & Youhua Qian

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  1. Haolan Wang
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Correspondence to Youhua Qian.

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Wang, H., Qian, Y. Complex bursting dynamics in a Rayleigh–Liénard oscillator. Nonlinear Dyn 112, 7679–7693 (2024). https://doi.org/10.1007/s11071-024-09455-5

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