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Title: Stochastic D-bifurcation for a damped sine-Gordon equation with noise

We investigate the stochastic bifurcation of a damped sine-Gordon equation with Dirichlet boundary conditions under the influence of multiplicative Gaussian white noise. Introducing a slow time scale, we derive the amplitude equations near the trivial solution by multiscale analysis. And the stationary probability density functions are formulated analytically using the stochastic averaging of energy envelope. The numerical calculations show that the system undergoes a stochastic D-bifurcation of energy envelope from a delta measure to new stationary measures when the control parameter crosses a critical point.
Authors:
;  [1] ;  [2]
  1. Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng 224051 (China)
  2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082 (China)
Publication Date:
OSTI Identifier:
22488533
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Advances; Journal Volume: 5; Journal Issue: 4; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; BOUNDARY CONDITIONS; CONTROL; DIRICHLET PROBLEM; MATHEMATICAL SOLUTIONS; PROBABILITY DENSITY FUNCTIONS; SINE-GORDON EQUATION