Stability of synchronous states in sparse neuronal networks
Neurons and Cognition
2020-02-04 v1 Dynamical Systems
Adaptation and Self-Organizing Systems
Abstract
The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable class of sparse random matrices, randomness being a consequence of the network structure. A detailed analysis, which includes also the study of finite-amplitude perturbations, is performed in the limit of narrow pulses, finding that the stability depends crucially on the relative pulse-width. This has implications for the overall property of the asynchronous (balanced) regime.
Keywords
Cite
@article{arxiv.2002.00448,
title = {Stability of synchronous states in sparse neuronal networks},
author = {Afifurrahman and Ekkehard Ullner and Antonio Politi},
journal= {arXiv preprint arXiv:2002.00448},
year = {2020}
}
Comments
9 pages, 7 figures