Bifurcation of limit cycles in a near Hamiltonian system with a cusp of order two and a saddle

چکیده مقاله

In this paper the asymptotic expansion of first-order Melnikov function of a heteroclinic loop connecting a cusp of order two and a hyperbolic saddle for a planar near-Hamiltonian system is given. Next, we consider the limit cycle bifurcations of a hyper-elliptic Lienard system with this kind of heteroclinic loop and study the least upper bound of limit cycles bifurcated from the period annulus inside the heteroclinic loop, from the heteroclinic loop itself and the center. Wend that at most three limit cycles can be bifurcated from the period annulus, also we give different distribution of bifurcated limit cycles.