• Corpus ID: 231846530

The effect of pulse width on the dynamics of pulse-coupled oscillators

  title={The effect of pulse width on the dynamics of pulse-coupled oscillators},
  author={Afifurrahman and Ekkehard Ullner and Antonio Politi},
The idealisation of neuronal pulses as δ -spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse-width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions, inspired by leaky integrate-and-fire… 



Linear stability in networks of pulse-coupled neurons

A general approach to linear stability of pulse-coupled neural networks for generic phase-response curves and post-synaptic response functions and a mean-field approach developed under the hypothesis of an infinite network and small synaptic conductances and a “microscopic” approach which applies to finite but large networks.

Self-sustained irregular activity in an ensemble of neural oscillators

An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies and it is revealed that the dynamics of the order parameter is indeed high-dimensional.

Quantitative and qualitative analysis of asynchronous neural activity

The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics, and the distribution of interspike intervals turns out to be relatively long-tailed; a crucial feature required for the self-sustainment of the bursting activity in a regime where neurons operate on average (much) below threshold.

Stability of the splay state in pulse-coupled networks.

It is found that the splay state can be stable even for inhibitory coupling, and the spectrum of Floquet exponents turns out to consist of a number of "isolated" eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities.

Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons.

It is reported in this type of network that chaotic dynamics characterized by positive Lyapunov exponents can also be observed and it is shown that chaos occurs when the decay time of the synaptic currents is long compared to the synaptic delay, provided that the network is sufficiently large.

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

  • N. Brunel
  • Biology
    Journal of Computational Neuroscience
  • 2004
The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous

Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons

It is found that the neural network does not only exhibit a microscopic (single-neuron) stochastic-like evolution, but also a collective irregular dynamics (CID), which is a true thermodynamic phase, intrinsically different from the standard asynchronous regime.

Desynchronization in diluted neural networks.

The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated, and the paradox is solved by drawing an analogy with the phenomenon of "stable chaos" by observing that the stochasticlike behavior is "limited" to an exponentially long transient.

Macroscopic description for networks of spiking neurons

The results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network.

Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons

It is shown that an unstructured, sparsely connected network of model spiking neurons can display two fundamentally different types of asynchronous activity that imply vastly different computational properties.