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We analyze the effects of spatiotemporal noise on stationary pulse solutions (bumps) in neural field equations on planar domains. Neural fields are integrodifferential equations whose integral kernel describes the strength and polarity of…
We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…
We study the effects of additive noise on traveling pulse solutions in spatially extended neural fields with linear adaptation. Neural fields are evolution equations with an integral term characterizing synaptic interactions between neurons…
The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain's learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and…
We analyze the effects of noise on the traveling wave dynamics in neural fields. The noise influences the dynamics on two scales: first, it causes fluctuations in the wave profile, and second, it causes a random shift in the phase of the…
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…
We study the effects of propagation delays on the stochastic dynamics of bumps in neural fields with multiple layers. In the absence of noise, each layer supports a stationary bump. Using linear stability analysis, we show that delayed…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
We study the effects of noise-intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions,…
We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the…
Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the effect of noise on these models is one of the key open questions in computational…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
A general approach to consider spatially extended stochastic systems with correlations between additive and multiplicative noises subject to nonlinear damping is developed. Within modified cumulant expansion method, we derive an effective…
The influence of quantized electromagnetic fields on a nonrelativistic charged particle moving near a conducting plate is studied. We give a field-theoretic derivation of the nonlinear, non-Markovian Langevin equation of the particle by the…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of…