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An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable network activations within a limited critical range. In this range, the…
In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote…
Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive…
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…
Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the…
Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them have been variously…
We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…
We report the emergent dynamics of a community structured modular network of chaotic Hindmarsh-Rose (HR) neurons with inhibitory synapses. We find the inhibitory coupling between the neuronal modules lead to complete synchronization of…
Starting from a spectral expansion of the Fokker-Plank equation for the membrane potential density in a network of spiking neurons, a low-dimensional dynamics of the collective firing rate is derived. As a result a $n$-order ordinary…
How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been…
There is cognitive, neurological, and computational support for the hypothesis that defocusing attention results in divergent or associative thought, conducive to insight and finding unusual connections, while focusing attention results in…
In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the…
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 extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find…
Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics…
The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability…
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…
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…