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

Research output: Contribution to journalArticle


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.


External organisations
  • External Organization - Unknown
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
Pages (from-to)1021-1047
Issue number5
Publication statusPublished - 2006
Publication categoryResearch
Externally publishedYes