Related papers: Relaxation and self-sustained oscillations in the …
Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been…
Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
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…
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 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…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself,…
Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators is perturbed locally. Several asymptotic states of different frequencies can coexist at the same node. Here, we reveal the mechanism…
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 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 analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
The ability to understand and eventually predict the emergence of information and activation cascades in social networks is core to complex socio-technical systems research. However, the complexity of social interactions makes this a…
We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10-200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level…
We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are…
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…
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 revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…