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Sequential activation of neurons is a common feature of network activity during a variety of behaviors, including working memory and decision making. Previous network models for sequences and memory emphasized specialized architectures in…
A new mathematical model of memristive neural networks described by the partly diffusive reaction-diffusion equations with weak synaptic coupling is proposed and investigated. Under rather general conditions it is proved that there exists…
In this article, we are interested in the behavior of a fully connected network of $N$ neurons, where $N$ tends to infinity. We assume that the neurons follow the stochastic FitzHugh-Nagumo model, whose specificity is the non-linearity with…
All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We explore the ignition and spread of collective spontaneous…
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…
We study dynamics of a reverberating neural net by means of computer simulation. The net, which is composed of 9 leaky integrate-and-fire (LIF) neurons arranged in a square lattice, is fully connected with interneuronal communication delay…
Neural networks are able to extract information from the timing of spikes. Here we provide new results on the behavior of the simplest neuronal model which is able to decode information embedded in temporal spike patterns, the so called…
We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate…
We investigate the dynamics of a network consisting of an array of identical cortical units with nearest neighbor interactions under periodic arousal. Each unit consists of two interconnected populations of neurons tuned to a state in which…
The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…
Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated using model neurons with simple connection topology…
Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…
Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and…
We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively…
Recently, it has been shown that the communities in neuronal networks of the integrate-and-fire type can be identified by considering patterns containing the beginning times for each cell to receive the first non-zero activation. The…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
Understanding how contagions (information, infections, etc) are spread on complex networks is important both from practical as well as theoretical point of view. Considerable work has been done in this regard in the past decade or so.…
The dynamical responses of complex neuronal networks to external stimulus injected on a \emph{single} neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus…
We investigate heterogeneous coupling delays in complex networks of excitable elements described by the FitzHugh-Nagumo model. The effects of discrete as well as of uni- and bimodal continuous distributions are studied with a focus on…