title: Spatial pattern formation induced by Gaussian white noise.
abstract: The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable environmental disturbances, and (iii) a linear spatial coupling component, which provides spatial coherence and takes into account diffusion mechanisms. We investigate these dynamics using analytical tools, such as mean-field theory, linear stability analysis and structure function analysis, and use numerical simulations to confirm these analytical results.
authors.affiliation: Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili, Politecnico di Torino, Turin, Italy. stefania.scarsoglio@polito.it
authors.forename: Stefania
authors.initials: S
authors.lastname: Scarsoglio
authors.forename: Francesco
authors.initials: F
authors.lastname: Laio
authors.forename: Paolo
authors.initials: P
authors.lastname: D'Odorico
authors.forename: Luca
authors.initials: L
authors.lastname: Ridolfi
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D017753:Ecosystem; D008954:Models, Biological; D008962:Models, Theoretical; D019368:Nature; D013269:Stochastic Processes