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
  • [11] Costa A.(2017)Effects of combined harmonic and random excitations on a Brusselator model Eur. Phys. J. B 90 2557-2561
  • [12] Quelhas M.(2018)Active vibration suppression of a novel airfoil model with fractional order viscoelastic constitutive relationship J. Sound Vib. 432 1569-1576
  • [13] Francesco M.(2018)Stability analysis of a fractional-order predator–prey model incorporating a constant prey refuge and feedback control Adv. Differ. Equ. 2018 157-161
  • [14] Wang Z.(2014)Nonlinear dynamic characteristics and optimal control of giant magnetostrictive laminated plate subjected to in-plane stochastic excitation AIP Adv. 4 524-529
  • [15] Xu Y.(2005)On double-peak probability density functions of a Duffing oscillator under narrow-band random excitations Acta Phys. Sin. 54 257-264
  • [16] Yang H.(2006)On double peak probability density functions of Duffing oscillator to combined deterministic and random excitations Appl. Math. Mech. 27 1324-1329
  • [17] Xu Y.(2011)Stochastic bifurcations in Duffing–van der Pol oscillator with Lévy stable noise Acta Phys. Sin. 60 1121-1135
  • [18] Li H.(2011)Stochastic bifurcations in a bistable Duffing–Van der Pol oscillator with colored noise Phys. Rev. E 83 62-69
  • [19] Wang H.(2010)Stochastic bifurcations and coherence-like resonance in a self-sustained bistable noisy oscillator Phys. Rev. E 81 109-115
  • [20] Jia W.(2013)Three-peak P-bifurcations in stochastically excited van der Pol–Duffing oscillator Sci. China, Ser. G, Phys. Mech. Astron. 43 48-65
12345678910