Bifurcation Of Limit Cycles From A Heteroclinic Loop With Two Cusps

In this paper, we mainly the bifurcation of limit cycles from a heteroclinic loop with two cusps.In Chapter one, we introduce the background of our research, main topics and results that we will study in the following chapters.In Chapter two, we introduce the bifurcation of limit cycles from a homoclinic loop with a cusp which are studied by Han et al and list some results.In Chapter three, we study the expansion of the first Melnikov function for general near-Hamiltonian systems near a Heteroclinic loop with two cusps of order2, obtain the formulas for the first coefficients appearing in the expansion, and establish some bifurcation theorems on the number of limit cycles.In Chapter four, we study the expansion of the first Melnikov function for general near-Hamiltonian systems near a Heteroclinic loop with a cusp of order1and a cusp of order2, obtain the formulas for the first coefficients appearing in the expansion, and establish some bifurcation theorems on the number of limit cycles. We also give a application example.