Chaos Research of Asymmetric System Based on Melnikov Method

摘要

Based on Helmholtz-Duffing which is a typical nonlinear asymmetric dynamical system, According to homoclinic bifurcations, prerequisites for chaos motion are obtained by use of Melnikov theory. As a result of verifying the analytic solutions, the safe basin and the phenomena of erosion of the safe basin are simulated by numerical method in the end. The research indicates that the value range of is closely related to the area influenced by the value itself: when is located in the range of from zero to one, the left part of system is mainly affected; when is larger than one, the right part of system is mainly affected. For the same symmetry parameter, there exist a critical frequency at which the threshold value of the amplitudes of both left and right part of system are equal.