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Limit cycle bifurcations by perturbing a cubic reversible Hamiltonian system with multiple switching curves

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  • Yang, Jihua

Abstract

This paper investigates the limit cycle problems in a cubic reversible isochronous Hamiltonian system under nth-degree polynomial nonsmooth perturbations with switching curves x=0 and x=43y2. The upper and lower bounds of the number of limit cycles are derived through the first order Melnikov function and its asymptotic expansion.

Suggested Citation

  • Yang, Jihua, 2026. "Limit cycle bifurcations by perturbing a cubic reversible Hamiltonian system with multiple switching curves," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015826
    DOI: 10.1016/j.chaos.2025.117569
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    References listed on IDEAS

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    1. Azhdari, Meysam & Binazadeh, Tahereh, 2022. "A novel adaptive SMC strategy for sustained oscillations in nonlinear sandwich systems based on stable limit cycle approach," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Llibre, Jaume & Valls, Claudia, 2024. "The phase portrait of all polynomial Liénard isochronous centers," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Hakimi, A.R. & Azhdari, M. & Binazadeh, T., 2021. "Limit cycle oscillator in nonlinear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    4. Xiong, Yanqin & Hu, Jianqiang, 2019. "A class of reversible quadratic systems with piecewise polynomial perturbations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    5. Azhdari, Meysam & Binazadeh, Tahereh, 2023. "Robust limit cycle control for finite-time generation of sustained oscillations in nonlinear systems with mixed dead-zone and saturation," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Yang, Jihua, 2020. "Limit cycles appearing from the perturbation of differential systems with multiple switching curves," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    Full references (including those not matched with items on IDEAS)

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