## Integrate and fire neural networks, piecewise contractive maps and limit cycles.

- Eleonora Catsigeras, Pierre Guiraud
- Journal of mathematical biology
- 2013

2 Excerpts

- Published 2008

We prove that a topologically generic network (an open and dense set of networks) of three or more inhibitory neurons have periodic behavior with a finite number of limit cycles that persist under small perturbations of the structure of the network. The network is modeled by the Poincaré transformation which is piecewise continuous and locally contractive on a compact region B of a finite dimensional manifold, with the separation property: it transforms homeomorphically the different continuity pieces of B into pairwise disjoint sets. PACS 2008 codes: 87.19 lj, 87.19 ll, 87.19 lm MSC 2000 92B20, 34C25, 37G15, 24C28

@inproceedings{Catsigeras2008ContractivePC,
title={Contractive piecewise continuous maps modeling networks of inhibitory neurons},
author={E. Catsigeras and A. Rovella and R. Budelli},
year={2008}
}