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

Ranran Jia, Liqin Zhao

• 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.