Twenty-Six Crossing Limit Cycles Around One Singular Point in a Cubic Switching System

Abstract

In this paper, we obtain a lower bound for the maximum number of crossing limit cycles for cubic planar switching systems with two regions separated by a straight line. By pseudo Hopf bifurcation and [Formula: see text]-order Lyapunov constants, we prove that there exist cubic near-integrable switching systems with at least 26 small-amplitude limit cycles bifurcating from an elementary center after suitable perturbations. To the best of our knowledge, this is the best lower bound so far for the cubic class by using a first order analysis.