Eighteen limit cycles around two symmetric foci in a cubic planar switching polynomial system

In this paper, we present a cubic planar switching polynomial system with Z2-symmetry, and prove that such a system can exhibit at least 9 small-amplitude limit cycles around each of two symmetric foci, giving a total 18 limit cycles. This is a new lower bound for the number of limit cycles bifurcating in cubic switching polynomial systems around foci, simultaneously obtained around the same time when more limit cycles are achieved by perturbing a cubic switching integral system.