Adiabatic reduction near a bifurcation in stochastically modulated systems

Journal Article · Fri May 01 04:00:00 EDT 1998 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.57.5036· OSTI ID:627903

Drolet, F; Vinals, J ^[1]; Vinals, J ^[2]

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1. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida32306-4130 (United States)
2. Department of Chemical Engineering, FAMU-FSU College of Engineering, Tallahassee, Florida 32310-6046 (United States)

We reexamine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary solutions of the Fokker-Planck equation are obtained near threshold for the pitchfork and transcritical bifurcations. Correlations between fast variables and random modulation may shift the effective bifurcation point by an amount proportional to the intensity of the fluctuations. We also find that fluctuations of the fast variables above threshold are not always Gaussian and centered around the (deterministic) center manifold as was previously believed. Numerical solutions obtained for a few illustrative examples support these conclusions. {copyright} {ital 1998} {ital The American Physical Society}

• OSTI ID: 627903
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 5 Vol. 57; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BIFURCATION
FLUCTUATIONS
FOKKER-PLANCK EQUATION
NUMERICAL SOLUTION
RANDOMNESS
STOCHASTIC PROCESSES