Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system |
| |
Authors: | Ali Atabaigi Hamid RZ Zangeneh Rasool Kazemi |
| |
Institution: | Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran |
| |
Abstract: | This paper deals with the analytical property of the first Melnikov function for general Hamiltonian systems possessing a cuspidal loop of order 2 and its expansion at the Hamiltonian value corresponding to the loop. The explicit formulas for the first coefficients of the expansion have been given. We prove that at least 13 limit cycles can bifurcate from the cuspidal loop of order 2 under certain conditions. Then we consider the cyclicity of a cuspidal loop in some Liénard and Hamiltonian systems, and determine the number of limit cycles that can bifurcate from the perturbed system. |
| |
Keywords: | 34C07 34C08 37G15 34M50 |
本文献已被 ScienceDirect 等数据库收录! |