Related papers: Mean field methods for cortical network dynamics

We compute the firing rate of a leaky integrate-and-fire (LIF) neuron with stochastic conductance-based inputs in the limit when synaptic decay times are much shorter than the membrane time constant. A comparison of our analytical results…

We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in…

Mechanisms underlying the emergence of orientation selectivity in the primary visual cortex are highly debated. Here we study the contribution of inhibition-dominated random recurrent networks to orientation selectivity, and more generally…

Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of non-zero…

We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact…

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in…

We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However,…

We propose a computational model of neuron, called firing cell (FC), properties of which cover such phenomena as attenuation of receptors for external stimuli, delay and decay of postsynaptic potentials, modification of internal weights due…

The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. Open questions surround the basic nature of these correlations. In particular, what leads to…

We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We…

Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…

We studied the impact of a dynamical threshold on the f-I curve-the relationship between the input and the firing rate of a neuron-in the presence of background synaptic inputs. First, we found that, while the leaky integrate-and-fire model…

Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We…

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…

Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome…

Kinetics of a balanced network of neurons with a sparse grid of synaptic links is well representable by the stochastic dynamics of a generic neuron subject to an effective shot noise. The rate of delta-pulses of the noise is determined…

In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an edge of chaos perspective. Our investigation…

We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of…