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Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop

Author

Listed:
  • Erli Zhang

    (School of Statistics and Big Data, Zhengzhou College of Finance and Economics, Zhengzhou 450044, China)

  • Stanford Shateyi

    (Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa)

Abstract

This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m . By analyzing the asymptotic expansion (AE) of the Melnikov function with first-order M ( h ) near the generalized heteroclinic loop (HL), we utilize the expansions of the corresponding generators. This approach allows us to establish both lower and upper bounds for the quantity of limit cycles in the perturbed system. Our analysis involves a combination of expansion techniques, derivations, and divisions to derive these findings.

Suggested Citation

  • Erli Zhang & Stanford Shateyi, 2023. "Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop," Mathematics, MDPI, vol. 11(18), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3944-:d:1241632
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    References listed on IDEAS

    as
    1. Liang, Feng & Han, Maoan, 2012. "Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 454-464.
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