相关论文: Dynamical phase separation on rhythmogenic neurona…

We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over…

By extending a dynamical mean-field approximation (DMA) previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 41903 (2003)], we have developed a semianalytical theory which takes into account a wide range of couplings in a…

We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…

It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are…

Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…

We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading…

We investigate the dynamics of a neural network where each neuron evolves according to the combined effects of deterministic integrate-and-fire dynamics and purely inhibitory coupling with K randomly-chosen "neighbors". The inhibition…

Realizations of low firing rates in neural networks usually require globally balanced distributions among excitatory and inhibitory links, while feasibility of temporal coding is limited by neuronal millisecond precision. We show that…

Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…

Criticality can be exactly demonstrated in certain models of brain activity, yet it remains challenging to identify in empirical data. We trained a fully connected deep neural network to learn the phases of an excitable model unfolding on…

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems…

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…

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…

We study the collective dynamics of an ensemble of coupled identical FitzHugh--Nagumo elements in their excitable regime. We show that collective firing, where all the elements perform their individual firing cycle synchronously, can be…

The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…

This work is part of an effort to understand the neural basis for our visual system's ability, or failure, to accurately track moving visual signals. We consider here a ring model of spiking neurons, intended as a simplified computational…

The mammalian brain could contain dense and sparse network connectivity structures, including both excitatory and inhibitory neurons, but is without any clearly defined output layer. The neurons have time constants, which mean that the…

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function,…

In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since…