Onset of oscillatory instabilities under stochastic modulation

Journal Article · Mon Sep 01 04:00:00 EDT 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.56.2649· OSTI ID:664481

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

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1. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052 (United States)
2. Department of Chemical Engineering, FAMU-FSU College of Engineering, Tallahassee, Florida 32310 (United States)

We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the bifurcation and in the modulation amplitude. Stability boundaries are computed by either solving the stationary Fokker-Planck equation on the center manifold of the underlying deterministic system whenever possible, or by direct numerical solution otherwise. If the modulation amplitude has a stochastic component, the primary bifurcation is always to standing waves at a value of the control parameter that depends on the intensity of the fluctuations. More precisely, and to contrast our results with the case of a deterministic periodic forcing, the onset of instability in the standing-wave regime is shifted from its deterministic location, and the region of primary bifurcation to traveling waves disappears, yielding instead standing waves at negative values of the control parameter. {copyright} {ital 1997} {ital The American Physical Society}

• Research Organization: Florida State University
• DOE Contract Number: FG02-85ER25000
• OSTI ID: 664481
• 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: 3 Vol. 56; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
AMPLITUDES
BIFURCATION
CONTROL
FLUCTUATIONS
FOKKER-PLANCK EQUATION
INSTABILITY
MODULATION
O GROUPS
RANDOMNESS
STANDING WAVES
STOCHASTIC PROCESSES
TRAVELLING WAVES