THE APPROXIMATE SOLUTION OF STOCHASTIC VAN DER POL - DUFFING SYSTEM WITH TIME DELAY BY SECOND ORDER STOCHASTIC AVERAGING METHOD

Abstract

The paper shows that the approximate solution of the Van der PolDuffing system with time delay subjected to the white noise can be found by the second order stochastic averaging method. The stochastic system with time delay is transformed into the stochastic non-delay equation in Ito sense in accordance with the hypothesis that there are some slowly varying processes. Then the higher order stochastic averaging method is artfully applied to find the stationary probability density function for the system. The analytical results are verified by numerical simulation results.