Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

被引：0
作者：
Yajie Li
Zhiqiang Wu
Guoqi Zhang
Feng Wang
Yuancen Wang
机构：
[1] Henan University of Urban Construction,Department of Mathematics and Physics
[2] Tianjin University,Department of Mechanics, School of Mechanical Engineering
[3] Tianjin University,Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control
来源：
Advances in Difference Equations | / 2019卷
关键词：
Stochastic P-bifurcation; Fractional time-delay feedback; Gaussian white noise; Transition set; Monte Carlo simulation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.
引用
收藏
相关论文
共 161 条
[41]  
Fang T.(2015)Dynamical analysis of Duffing oscillator with fractional-order feedback with time delay Chin. Phys. B 24 29-41
[42]  
Rong H.(2008)Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback J. Comput. Appl. Math. 213 undefined-undefined
[43]  
Wang X.(2014)Bifurcation analysis in van der Pol’s oscillator with delayed feedback Chin. Phys. B 23 undefined-undefined
[44]  
Meng G.(2013)Hopf bifurcation control for a coupled nonlinear relative rotation system with time-delay feedbacks Int. J. Non-Linear Mech. 48 undefined-undefined
[45]  
Xu W.(2013)Stationary response of Duffing oscillator with hardening stiffness and fractional derivative J. Vib. Control 19 undefined-undefined
[46]  
Fang T.(2012)First-passage failure of single-degree-of-freedom nonlinear oscillators with fractional derivative Commun. Nonlinear Sci. Numer. Simul. 17 undefined-undefined
[47]  
Gu R.(2016)Primary resonance of Duffing oscillator with two kinds of fractional-order derivatives Chin. Phys. B 25 undefined-undefined
[48]  
Xu Y.(2014)Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation Theor. Appl. Mech. Lett. 4 undefined-undefined
[49]  
Hao M.(1997)Stochastic response of fractional-order van der Pol oscillator J. Eng. Mech. 123 undefined-undefined
[50]  
Yang Z.(2012)Random vibration of systems with frequency-dependent parameters or fractional derivatives Fract. Calc. Appl. Anal. 15 undefined-undefined
12345678910