Limit cycle bifurcations near a generalized homoclinic loop in piecewise smooth systems with a hyperbolic saddle on a switch line

摘要

In this paper, we suppose a planar piecewise Hamiltonian system has a generalized homoclinic loop with a hyperbolic saddle on a switch line, and assume that there are two families of periodic orbits on both sides of the loop. Under perturbations we first give the expansion of the first Melnikov function near the loop. Then by using the first coefficients in the expansion, we study the number of limit cycles bifurcating from the homoclinic loop.