Limit Cycle Bifurcations in Perturbations of a Reversible Quadratic System with a Non-rational First Integral

Abstract

This paper investigates the Hopf cyclicity of a piecewise smooth quadratic polynomial system by Melnikov function method, whose unperturbed system is a concrete reversible quadratic system with a center at the origin and with a non-rational first integral. By comparing the obtained result for the piecewise case with the result for the smooth case, it shows that the piecewise system can have at least four more limit cycles around the origin than the smooth one.