Stochastic Spatiotemporal Intermittency and Noise-Induced Transition to an Absorbing Phase

Abstract

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.Spatiotemporal chaos (STC) is a complex behavior, common to many spatially extended nonlinear dynamical systems [1][2][3][4]. This behavior is characterized by a combination of chaotic time evolution and spatial incoherence made evident by correlations decaying both in space and time. In spite of considerable theoretical and experimental effort devoted to give a precise definition of STC and its different regimes, the present status is still unsatisfactory. A possible strategy to make progress in the understanding of STC is to investigate scenarios based on simple models, with few controlled ingredients, that reproduce the spatio-temporal structures under study. Such models are instrumental in searching for generic mechanisms leading to such complex behavior. Among the available scenarios, few of them consider the framework of stochastic partial differential equations (SPDE) [5][6][7] to describe STC. A successful example is, however, the mapping of the Kuramoto-Shivashinsky equation (describing a STC regime named phase turbulence) to the stochastic model of surface growth known as KardarParisi-Zhang equation [8].A particular instance of STC is a regime called spatiotemporal intermittency (STI) which is present in a large variety of systems [9][10][11][12]. Generally speaking, this regime is a chaotic spatiotemporal evolution (the turbulent phase) irregularly and continuously interrupted by the spontaneous formation of domains with a wide range of sizes and lifetimes, where the behavior is ordered (laminar). The borders of the laminar regions propagate as fronts and eventually cause the collapse of the corresponding region into the turbulent background. There are strong indications that the STI regime has many features in common with phenomena of probabilistic nature. For example, it appears in some systems that critical exponents at the onset of STI are in the universality class of directed percolation [13]. STI has also been related to nucleation [11], another process associated with stochastic fluctuations. However, no description of STI in terms of SPDEs has been put forward so far.The purpose of this Letter is to introduce a model, entirely based on a simple SPDE, that describes the main features of STI, and report the existence of a noise induced transition from laminarity to STI. The laminar phase is associated to an equilibrium state called absorbing in the SPDE parlance. The role of the turbulent phase is played by a strongly fluctuating sta...

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