Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m


主讲人:杨俊敏 河北师范大学教授




内容介绍:In this paper, we study the explicit expansion of the first order Melnikov ?function near a double homo-clinic loop passing through a nilpotent saddle of ?order min a near-Hamiltonian system. For any positive integer m(m ≥1), we derive ?the formulas of the coefficients in the expansion, which can be used to study ?the limit cycle bifurcations for near-Hamiltonian systems. In particular, for m ?=2, we use the coefficients to consider the limit cycle bifurcations of general ?near-Hamiltonian systems and give the existence conditions for 10, 11, 13, 15 ?and 16 (11, 13 and 16, respectively) limit cycles in the case that the ?homoclinic loop is of cuspidal type (smooth type, respectively) and their ?distributions. As an application, we consider a near-Hamiltonian system with a ?nilpotent saddle of order 2and obtain the lower bounds of the maximal number of ?limit cycles.