In this review, we provide a concise summary of several important mathematical results for
stochastic travelling waves generated by monostable and bistable reaction-diffusion …

In this paper we present a framework in which one can rigorously study the effect of spatio-
temporal noise on traveling waves, stationary patterns, and oscillations that are invariant …

The aim of the paper is to address the behavior in large population of diffusions interacting
on a random, possibly diluted and inhomogeneous graph. This is the natural continuation of …

We use stochastic neural field theory to analyze the stimulus-dependent tuning of neural
variability in ring attractor networks. We apply perturbation methods to show how the neural …

We introduce a variational method for analyzing limit cycle oscillators in R^d driven by
Gaussian noise. This allows us to derive exact stochastic differential equations for the …

We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh–Nagumo
equations with additive noise. Special attention is given to the effect of small noise on the …

We consider reaction-diffusion equations that are stochastically forced by a small
multiplicative noise term. We show that spectrally stable traveling wave solutions to the …

Inspired by applications, we consider reaction–diffusion equations on R that are
stochastically forced by a small multiplicative noise term that is white in time, coloured in …

We study the dynamics of waves, oscillations, and other spatio-temporal patterns in
stochastic evolution systems, including SPDE and stochastic integral equations …

We develop a generalized variational method for analyzing wandering bumps in a
stochastic neural field model defined on some domain U. For concreteness, we take U= S 1 …