Bifurcation analysis on a class of \(Z_{2}\)-equivariant cubic switching systems showing eighteen limit cycles
In this paper, the authors apply the method developed for computing the Lyapunov constants of planar switching systems associated with an elementary singular point to study bifurcations of limit cycles in a cubic switching system. A complete classification on the center conditions and 16 limit cycles are obtained around the two foci of this system. Further, with this method, the authors construct an example of a cubic switching system to show the existence of 18 small-amplitude limit cycles bifurcating from the centers. This is a new lower bound on the maximal number of small-amplitude limit cycles obtained in such cubic switching systems. Finally, a method to show the realization of the 18 limit cycles is presented.
scientific article; zbMATH DE number 6987658
scientific article