Work

A General Framework for Stochastic Traveling Waves and Patterns, with Application to Neural Field Equations

Year: 2016

Type: article

Abstract: In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular, the framework can incorporate versions of the stochastic neural field equation that may exhibit traveling fronts, pulses, or stationary patterns. To do this, we first formulate a local SDE that describes the position of the stochastic wave up until a discontinuity time, at which point the position of the wave may jump. We then study the local stability of this stochastic front, obtaining a result that recovers a well-known deterministic result in the small-noise limit. We finish with a study of the long-time behavior of the stochastic wave.

Source: SIAM Journal on Applied Dynamical Systems

DOI: 10.1137/15m102856x

Authors: J. Inglis, J. MacLaurin

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, European Research Council, Seventh Framework Programme

Awards: Brain-inspired multiscale computation in neuromorphic hybrid systems, G4186492805, G4805439115, MATHEmatics of Multi-level Anticipatory Complex Systems, G9000178569

OpenAlex ID: W796303710

FWCI: 4.735

Cites: 34

Cited by: 41

Related to: 10