TY - JOUR
T1 - Onset of oscillatory instabilities under stochastic modulation
AU - Drolet, François
AU - Viñals, Jorge
PY - 1997
Y1 - 1997
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.
UR - http://www.scopus.com/inward/record.url?scp=0001292567&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0001292567&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.56.2649
DO - 10.1103/PhysRevE.56.2649
M3 - Article
AN - SCOPUS:0001292567
SN - 1063-651X
VL - 55
SP - 2649
EP - 2663
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 3
ER -