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Title: Delay-induced stochastic bifurcations in a bistable system under white noise

In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.
Authors:
; ;  [1] ;  [2]
  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072 (China)
  2. Department of Mathematics and Information Science, Chang'an University, Xi'an 710086 (China)
Publication Date:
OSTI Identifier:
22482311
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAPMAN-KOLMOGOROV EQUATION; COMPUTERIZED SIMULATION; FEEDBACK; FOKKER-PLANCK EQUATION; MARKOV PROCESS; NOISE; OSCILLATORS; PROBABILITY DENSITY FUNCTIONS; RANDOMNESS; TIME DELAY