External Fluctuations in a Pattern-Forming Instability
J. Garcia-Ojalvo (Georgia Institute of Technology), J.M. Sancho, (Univ. de Barcelona)
TL;DR
This paper investigates how external fluctuations influence pattern formation using a stochastic Swift-Hohenberg model with multiplicative noise, revealing a noise-controlled shift in the bifurcation point and explaining it analytically.
Contribution
It introduces a stochastic Swift-Hohenberg model with space-correlated noise to analyze external fluctuation effects on pattern formation, providing both numerical and analytical insights.
Findings
Noise shifts the bifurcation point in pattern formation.
The magnitude of the shift decreases with noise correlation length.
Numerical simulations confirm the analytical predictions.
Abstract
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e. produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.
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