Melnikov Method in Chaos Analysis of Asymmetric Dynamic System

Abstract

Abstract:

Abstract： Based on HelmholtzDuffing oscillator which is an asymmetric doublepotentialwell dynamical system, the potential function and phase plane of degenerated Hamilton system at different asymmetric parameters of σ were analyzed. Then according to the Melnikov theory, the threshold values of the left and right homoclinic orbits of the nonautonomous system excited by the harmonic force were deduced. By virtue of numerical simulation, the safe basin was obtained and the erosion phenomenon of safe basin along with the variation of excitation amplitude was observed, which verified the correctness of the analytical results. The research shows that when σ is between 0 and 1, the left half of the system is mainly affected, and the condition is on the contrary when σ is larger than 1. For the same asymmetric parameter σ, there exists a critical frequency at which the threshold value of both left and right half of system are equal.

Key words: asymmetry, Melnikov method, chaos, safe basin

CLC Number:

U 661.3

LIU Yachong1，HU Ankang1,2，HAN Fenglei1，WANG Chunhui1，LUYu1. Melnikov Method in Chaos Analysis of Asymmetric Dynamic System[J]. Journal of Shanghai Jiaotong University, 2015, 49(04): 475-480.

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