Related papers: Propagation of chaos in neural fields

A neural field models the large scale behaviour of large groups of neurons. We extend results of van Gils et al. [2013] and Dijkstra et al. [2015] by including a diffusion term into the neural field, which models direct, electrical…

This paper develops a non-asymptotic, local approach to quantitative propagation of chaos for a wide class of mean field diffusive dynamics. For a system of $n$ interacting particles, the relative entropy between the marginal law of $k$…

The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…

If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…

Driven by the explosion of data and the impact of real-world networks, a wide array of mathematical models have been proposed to understand the structure and evolution of such systems, especially in the temporal context. Recent advances in…

We consider interacting systems particle driven by i.i.d. fractional Brownian motions, subject to irregular, possibly distributional, pairwise interactions. We show propagation of chaos and mean field convergence to the law of the…

We recently introduced idealized mean-field models for networks of integrate-and-fire neurons with impulse-like interactions -- the so-called delayed Poissonian mean-field models. Such models are prone to blowups: for a strong enough…

While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…

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…

The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to…

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…

Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with…

Circadian rhythmicity lies at the center of various important physiological and behavioral processes in mammals, such as sleep, metabolism, homeostasis, mood changes and more. It has been shown that this rhythm arises from self-sustained…

We consider large systems of particles interacting through rough but bounded interaction kernels. We are able to control the relative entropy between the $N$-particle distribution and the expected limit which solves the corresponding Vlasov…

Sensory perception (e.g. vision) relies on a hierarchy of cortical areas, in which neural activity propagates in both directions, to convey information not only about sensory inputs but also about cognitive states, expectations and…

Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the robustness of these patterns with respect to noise is one of the key open questions in…

Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…

We introduce a framework to prove propagation of chaos for interacting particle systems with singular, density-dependent interactions, a classical challenge in mean-field theory. Our approach is to define the dynamics implicitly via a…

Diluted neural networks with continuous neurons and nonmonotonic transfer function are studied, with both fixed and dynamic synapses. A noisy stimulus with periodic variance results in a mechanism for controlling chaos in neural systems…