On the Number of Limit Cycles Bifurcating from the Linear Center with a Cubic Switching Curve

• Ranran Jia ^[1] ; Liqin Zhao ^[1]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-00986-1
• Enlaces
  • Texto completo
• Resumen

  • This paper studies the bifurcations of limit cycles from the system x˙ = y, y˙ = −x with the switching curve y = x3/3 − x under the perturbations of arbitrary polynomials of x and y with degree n. We obtain the lower bound and upper bound of the maximum number of limit cycles bifurcating from h ∈ (0, 3/2) if the first order Melnikov function is not identically 0. When the degree of perturbing terms is low, we obtain a precise result on the number of zeros of the first order Melnikov function. We also give an example to illustrate our result.

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