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

Journal Article · Wed Apr 15 00:00:00 EDT 2015 · AIP Advances

DOI:https://doi.org/10.1063/1.4918302· OSTI ID:22488533

Huang, Qiongwei; Xue, Changfeng ^[1]; Tang, Jiashi ^[2]

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1. Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng 224051 (China)
2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082 (China)

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.

• OSTI ID: 22488533
• Journal Information: AIP Advances, Vol. 5, Issue 4; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 2158-3226
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BIFURCATION
BOUNDARY CONDITIONS
CONTROL
DIRICHLET PROBLEM
MATHEMATICAL SOLUTIONS
PROBABILITY DENSITY FUNCTIONS
SINE-GORDON EQUATION