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 existence and characterisation of noise-driven bifurcations from the spatially
homogeneous stationary states of a nonlinear, non-local Fokker–Planck type partial …

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 …

A system of partial differential equations representing stochastic neural fields was recently
proposed with the aim of modelling the activity of noisy grid cells when a mammal travels …

The activity generated by an ensemble of neurons is affected by various noise sources. It is
a well-recognised challenge to understand the effects of noise on the stability of such …

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

Stochastic dynamics has emerged as one of the key themes ranging from models in
applications to theoretical foundations in mathematics. One class of stochastic dynamics …

In this paper we establish the meta-stability of traveling waves for a class of reaction-
diffusion equations forced by a multiplicative noise term. In particular, we show that the …

We study pattern formation in class of a large-dimensional neural networks posed on
random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions …

Neural field models are nonlinear integro-differential equations for the evolution of neuronal
activity, and they are a prototypical large-scale, coarse-grained neuronal model in …