Spatiotemporal intermittency arises in several models of natural phenomenon. Among them there are reaction-diffusion equations (of the catalysis problem [zimm97b]), or even in Ginzburg-Landau equation (which models most extended transition to oscillatory behaviour [chate]). The typical patterns which arise in this regime consists of regions visiting a laminar phase, interspeded by a spatially chaotic state, whose borders move and invade the former (check how these patterns look in a shell). Thus the system never relaxes to the stable laminar phase. We have approached this problem by modelling this phenomenon with a stochastic extended model. Our model is based on a gradient flow governed by a bistable potential, together with a multiplicative Gaussian white noise term. The main results include the reversal of a stochastic front motion increase of the noise intensity, and the phase transtion from a laminar state to the complex spatiotemporal intermittency. We are able to characterize this transition analytically with a mean-field analysis.
References
We introduce a stochastic partial differential equation capable of reproducing the main features of spatiotemporal intermittency (STI). Additionally the model displays a noise induced transition from laminarity to the STI regime. We show by numerical simulations and a mean-field analysis that for high noise intensities the system globally evolves to a uniform absorbing phase, while for noise intensities below a critical value spatiotemporal intermittence dominates. A quantitative computation of the loci of this transition in the relevant parameter space is presented.