Vol 8: Linear stability in networks of pulse-coupled neurons.Report as inadecuate



 Vol 8: Linear stability in networks of pulse-coupled neurons.


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This article is from Frontiers in Computational Neuroscience, volume 8.AbstractIn a first step toward the comprehension of neural activity, one should focus on the stability of the possible dynamical states. Even the characterization of an idealized regime, such as that of a perfectly periodic spiking activity, reveals unexpected difficulties. In this paper we discuss a general approach to linear stability of pulse-coupled neural networks for generic phase-response curves and post-synaptic response functions. In particular, we present: 1 a mean-field approach developed under the hypothesis of an infinite network and small synaptic conductances; 2 a -microscopic- approach which applies to finite but large networks. As a result, we find that there exist two classes of perturbations: those which are perfectly described by the mean-field approach and those which are subject to finite-size corrections, irrespective of the network size. The analysis of perfectly regular, asynchronous, states reveals that their stability depends crucially on the smoothness of both the phase-response curve and the transmitted post-synaptic pulse. Numerical simulations suggest that this scenario extends to systems that are not covered by the perturbative approach. Altogether, we have described a series of tools for the stability analysis of various dynamical regimes of generic pulse-coupled oscillators, going beyond those that are currently invoked in the literature.



Author: Olmi, Simona; Torcini, Alessandro; Politi, Antonio

Source: https://archive.org/







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