Stability of the splay state in pulse--coupled networks

Details Stability of the splay state in pulse--coupled networks Stability of the splay state in pulse--coupled networks

2007-05-19

arxiv.org/abs/0705.2811v1

Phys. Rev. E 76, 046102 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

13 pages, 10 figures, submitted for pubblication to Physical Review E

Scientific paper

10.1103/PhysRevE.76.046102

The stability of the dynamical states characterized by a uniform firing rate ({\it splay states}) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse--width and the inter-spike interval. More precisely, the spectrum of Floquet exponents turns out to consist of three components: (i) one that coincides with the predictions of the mean-field analysis [Abbott-van Vreesvijk, 1993]; (ii) a component measuring the instability of "finite-frequency" modes; (iii) a number of "isolated" eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities (the Floquet exponent being proportional to the network size). Finally, as a side result, we find that the splay state can be stable even for inhibitory coupling.

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