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Abstract

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.



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Issue: Vol 2 No 2 (2018)
Page No.: 102-109
Published: May 18, 2019
Section: Original Research
DOI: https://doi.org/10.32508/stdjns.v2i2.742

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Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Duong, H., Nguyen, A., & Nguyen, D. (2019). Applying higher order stochastic averaging method to the Van der Pol system with timedelay under random excitation. Science & Technology Development Journal: Natural Sciences, 2(2), 102-109. https://doi.org/https://doi.org/10.32508/stdjns.v2i2.742

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