Stochastic analysis of a noisy oscillator (Q756273)

The author studies the behaviour of the generalized Van der Pol oscillator \[ d^ 2x/dt^ 2=-x+[\alpha -\gamma x^ 2-\delta (dx/dt)^ 2] dx/dt+\xi (t), \] where \(\xi\) (\(\cdot)\) is Gaussian white noise. It is shown that \(\alpha =0\) is a bifurcation point of this oscillator provided that \(\gamma \delta <0\). The proof uses the complex stochastic averaging technique.