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Intermittency, metastability and coarse graining for coupled deterministic-stochastic lattice systems

Author

Summary, in English

We study the role of strong particle/particle interactions and stochastic fluctuations

emanating from the micro-/sub-grid scale, in the context of a simple prototype hybrid system con-

sisting of a scalar linear ordinary differential equation (ODE), coupled to a microscopic spin flip

Ising lattice system. Due to the presence of strong interactions in the lattice model, the mean-field

approximation of this system is a Fitzhugh-Nagumo-type system of ODEs. However, microscopic

noise and local interactions will significantly alter the deterministic and spatially homogeneous

mean-field Fitzhugh-Nagumo behaviours (excitable, bistable and oscillatory) and will yield cor-

responding regimes with phenomena driven by the interaction of nonlinearity and noise across

scales, such as strong intermittency, metastability and random oscillations. Motivated by these

observations we consider a class of stochastic numerical approximations based on systematic

coarse-grainings of stochastic lattice dynamics. The resulting stochastic closures give rise to com-

putationally inexpensive reduced hybrid models that capture correctly the transient and long-time

behaviour of the full system; this is demonstrated by detailed time series analysis that includes

comparisons of power spectra and auto- and cross-correlations in time and space, especially in

examples dominated by strong interactions between scales and fluctuations, such as nucleation,

intermittent and random oscillation regimes.

Publishing year

2006

Language

English

Pages

1021-1047

Publication/Series

Nonlinearity

Volume

19

Issue

5

Document type

Journal article

Publisher

London Mathematical Society / IOP Science

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 0951-7715