Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2649-2663 |
| Number of pages | 15 |
| Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 55 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 1997 |
| Externally published | Yes |
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Onset of oscillatory instabilities under stochastic modulation. / Drolet, François; Viñals, Jorge.
In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 55, No. 3, 01.01.1997, p. 2649-2663.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Onset of oscillatory instabilities under stochastic modulation
AU - Drolet, François
AU - Viñals, Jorge
PY - 1997/1/1
Y1 - 1997/1/1
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.56.2649
DO - 10.1103/PhysRevE.56.2649
M3 - Article
AN - SCOPUS:0001292567
VL - 55
SP - 2649
EP - 2663
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 3
ER -