Related papers: Wandering bumps in stochastic neural fields
Localized persistent cortical neural activity is a validated neural substrate of parametric working memory. Such activity `bumps' represent the continuous location of a cue over several seconds. Pyramidal (excitatory) and interneuronal…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established.…
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…
We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
We study localized patterns in an exact mean-field description of a spatially-extended network of quadratic integrate-and-fire (QIF) neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps,…
Volume transmission is an important neural communication pathway in which neurons in one brain region influence the neurotransmitter concentration in the extracellular space of a distant brain region. In this paper, we apply asymptotic…
Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit…
We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in…
We introduce a novel model for updating perceptual beliefs about the environment by extending the concept of Allostasis to the control of internal representations. Allostasis is a fundamental regulatory mechanism observed in animal…
Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the…
We introduce and analyze a class of neural network models motivated by the Drosophila central complex nervous system, designed to capture the emergence and dynamics of orientation-selective activity bumps. Starting from a biologically…
The propagation of signalling molecules within cellular networks is affected by network topology, but also by the spatial arrangement of cells in the networks. Understanding the collective reaction--diffusion behaviour in space of signals…
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…
Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them.…
We theoretically describe how weak signals may be efficiently transmitted throughout more than one frequency range in noisy excitable media by kind of stochastic multiresonance. This serves us here to reinterpret recent experiments in…
We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient…
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate…
We study heterogeneous distribution of gains in neural fields using techniques of quantum mechanics by exploiting a relationship of our model and the time-independent Schr\"{o}dinger equation. We show that specific relationships between the…