A general framework for stochastic traveling waves and patterns, with application to neural field equations

J. Inglis, J. MacLaurin

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

In this paper we present a general framework in which to rigorously study the effect of spatiotemporal 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.

Original languageEnglish (US)
Pages (from-to)195-234
Number of pages40
JournalSIAM Journal on Applied Dynamical Systems
Volume15
Issue number1
DOIs
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation

Keywords

  • Neural field
  • Pattern formation
  • Stability
  • Stochastic
  • Stochastic partial differential equation
  • Traveling pulse
  • Traveling wave

Fingerprint Dive into the research topics of 'A general framework for stochastic traveling waves and patterns, with application to neural field equations'. Together they form a unique fingerprint.

Cite this