Limit Cycles in Planar Piecewise Linear Differential Systems with Multiple Switching Curves

• 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. 24, Nº 3, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we provide the lower bound and upper bound of the maximum number of limit cycles Z(n) that planar piecewise linear differential systems with two zones separated by the curves y = ±x3(x > 0) under perturbation of arbitrary polynomials of x, y with degree n can have, where n ∈ N. By the first two order Melnikov functions, we achieve that 7 ≤ Z(1) ≤ 12, Z(2) = 5, Z(n) ≥ 3n for any n ≥ 3, and Z(n) ≤ 13n 2 + 11 when n is even, while Z(n) ≤ 13(n−1) 2 + 21 when n is odd.

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