Effects of time-delay feedback on steady state probability density of tri-stable van der Pol system

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (1) : 271-276.

DUAN Xuxing, WU Zhiqiang, LI Yajie

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Abstract

It is an important topicin stochastic dynamics and control to adjustsystem’s stochastic response characteristics using time-delay feedback. Here,to solve the design problem of controller parameters for multi-stable stochastic systems, effects of time-delay difference feedback on steady state probability density of a tri-stable van der Pol system under additive noise excitation were studied. The stochastic averaging method wasused to derive the analytical expression for the steady state probability density function of the system’s vibration amplitude, and then effects of time delay and feedback intensity on the system’s steady state probability density under given noise intensity were discussed, respectively. Results showedthat both feedback intensity and time delay can change topological structure of the system’s steady state probability density curve toadjust amplitude distribution of the system’s steady state response; the results of transition set calculation provide a direct guidance for choosing control parameters.

Key words

tri-stable van der Pol system / steady stateprobability density / time-delay feedback / noise excitation

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DUAN Xuxing, WU Zhiqiang, LI Yajie. Effects of time-delay feedback on steady state probability density of tri-stable van der Pol system[J]. Journal of Vibration and Shock, 2021, 40(1): 271-276

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