Open AccessApplying higher order stochastic averaging method to the Van der Pol system with timedelay under random excitation
Author(s) -
Hao Ngoc Duong,
Anh Thi Ngoc Nguyen,
Dung Quang Nguyen
Publication year - 2019
Publication title -
khoa học và công nghệ: tự nhiên
Language(s) - English
Resource type - Journals
ISSN - 2588-106X
DOI - 10.32508/stdjns.v2i2.742
Subject(s) - mathematics , monte carlo method , van der pol oscillator , excitation , statistical physics , probability density function , method of averaging , stationary distribution , physics , quantum mechanics , statistics , nonlinear system , markov chain
The paper investigated the Van der Pol system with time-delay under random excitation by the higher stochastic averaging method. The original system was expressed in terms without time-delay under the assumption that the state variabled of the system were slowly varying processed. Then the higher stochastic averaging method was applied on the approximation system. By this technique, the analytical expression of the stationary probability density function for the Van der Pol system with time-delay under random excitation was showed in higher order approximation for the first time. Effects of the parameter time-delay on the system’s response were investigated. The analytical results were suited well to numerical ones obtained by Monte-Carlo method. It was also showed that the higher order averaging solution was better than the one obtained by the traditional stochastic averaging method.