Behavior analysis of VanDerPol oscillator under the excitation of weak sinusoidal signal

Analysis the VanDerPol system through the methods of random Melnikov process function, we educe out the threshold of chaotic movement of VanDerPol non-linear system. It is found that the non-Gaussian color noise has little effect on the chaos character of this chaotic oscillator, well the values of parameters of the excitation weak sinusoidal signal appear much change of chaotic dynamic system. The tiny change to the amplitude and frequency of the excitation weak sinusoidal signal will induce the chaotic system behavior great differently, this character help us estimate parameters of weak sinusoidal signal. The numerical results confirm the conclusion that the chaotic oscillator is immune to zero mean non-Gaussian color noise for weak sinusoidal signal frequency and amplitude parameter estimate.