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Limit cycles near a compound cycle in a near-Hamiltonian system with smooth perturbations

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  • Yang, Junmin
  • Han, Maoan

Abstract

In this paper, we give a simple relation between the coefficients appearing in the expansions of n+2 (n∈Z+,n≥2) Melnikov functions near a compound cycle C(n), which can be used to simplify some computations. We further give some conditions for a general near-Hamiltonian system to have limit cycles as many as possible near C(n). Based on this, for a quintic Hamiltonian system with a compound cycle C(2) we prove that it can produce at least 72(n−2)+12(1+(−1)n) limit cycles near C(2) under polynomial perturbation of degree n(n≥2).

Suggested Citation

  • Yang, Junmin & Han, Maoan, 2024. "Limit cycles near a compound cycle in a near-Hamiltonian system with smooth perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005150
    DOI: 10.1016/j.chaos.2024.114963
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    References listed on IDEAS

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    1. Liu, Shanshan & Han, Maoan, 2023. "Limit cycle bifurcations near double homoclinic and double heteroclinic loops in piecewise smooth systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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