Stochastic Bifurcations in a Duffing System Driven by Additive Dichotomous Noises

WU Juan; XU Yong

doi:10.3879/j.issn.1000-0887.2015.06.003

Volume 36 Issue 6

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WU Juan, XU Yong. Stochastic Bifurcations in a Duffing System Driven by Additive Dichotomous Noises[J]. Applied Mathematics and Mechanics, 2015, 36(6): 593-599. doi: 10.3879/j.issn.1000-0887.2015.06.003

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Stochastic Bifurcations in a Duffing System Driven by Additive Dichotomous Noises

doi: 10.3879/j.issn.1000-0887.2015.06.003

WU Juan^1,2,
XU Yong¹

¹Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;²School of Mathematics & Information Science, Beifang University for Nationalities, Yinchuan 750021, P.R.China

Funds: The National Natural Science Foundation of China(11372247；11102157)

Received Date: 2014-12-30
Rev Recd Date: 2015-03-18
Publish Date: 2015-06-15

Abstract

Abstract

The stochastic bifurcations in a Duffing system driven by additive dichotomous noises were investigated. Firstly, the transition probability of the dichotomous noise states was deduced according to its statistical properties and then the dichotomous noise was simulated numerically. Secondly, the stationary joint probability density of the system displacement and speed and the stationary probability density of the displacement were calculated with the 4th-order Runge-Kutta algorithm. Then, through the study of the variation between unimodality and bimodality of the stationary probability density of the system displacement, it is found that specific states and certain intensity values of the additive dichotomous noise may induce stochastic bifurcations. Lastly, it is also observed that stochastic bifurcations may occur with the variations of the system asymmetric parameters.
- stochastic bifurcation,
- Duffing system,
- additive dichotomous noise,
- stationary probability density

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References(20)

References

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