2007/05/19 by Rüdiger Zillmer, Roberto Livi, Antonio Politi +1 · 4 citations
Biochemistry, Genetics and Molecular Biology · Neuroscience · Physics and Astronomy · #Neural dynamics and brain function #Photoreceptor and optogenetics research #cond-mat.dis-nn #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.76.046102
published as Phys. Rev. E 76, 046102 (2007) · 13 pages, 10 figures, submitted for pubblication to Physical Review E
arxiv created 2007/05/19 · openalex publication_date 2007/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The stability of the dynamical states characterized by a uniform firing rate (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 interspike 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 and van Vreesvijk, Phys. Rev. E 48, 1483 (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.