Response probability density functions of Duffing–Van der Pol vibro-impact system under correlated Gaussian white noise excitations

Chao Li, Wei Xu, Jinqian Feng and Liang Wang

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 6, 1269-1279

Abstract: This paper aims to investigate the stationary probability density functions (PDFs) of a Duffing–Van der Pol vibro-impact system excited by correlated Gaussian white noise. With the help of non-smooth transformation, the stationary PDFs are formulated analytically by the stochastic averaging of energy envelope. The analytical results are verified by numerical simulation results. Stochastic bifurcations for different parameters are considered, and several special PDF forms are observed in this paper. The first form is the shape of the PDF of total energy can be similar to a crater, which has a minimum and a maximum. The second one is the shape of the joint PDF with three peaks, that is to say, the section of joint PDF has three maximum and two minimum. In addition, the influence of the degree of the correlation of Gaussian white noises is explored.

Keywords: Vibro-impact system; Correlated Gaussian white noise; Non-smooth transformation; Stochastic averaging; Stationary PDFs; Stochastic bifurcation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:6:p:1269-1279

DOI: 10.1016/j.physa.2012.11.053

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