Linear stability in networks of pulse-coupled neurons

Frontiers in Computational Neuroscience

Alessandro eTorcini¹  Simona eOlmi¹  Antonio ePoliti² 

[1] Consiglio Nazionale delle Ricerche;University of Aberdeen;

关键词: synchronization;    neural networks;    pulse coupled neurons;    Floquet spectrum;    Linear stability analisys;    splay states;   

DOI  :  10.3389/fncom.2014.00008

来源: DOAJ

【 摘 要 】

In a first step towards the comprehension of neural activity, one should focus on
the stability of the possible dynamical states. Even the characterization of idealized regimes,
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: (i) a mean-field approach developed under the hypothesis
of an infinite network and small synaptic conductances; (ii) 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.

【 授权许可】

Unknown