IJPAM: Volume 61, No. 4 (2010)

CONTRACTIVE PIECEWISE CONTINUOUS MAPS
MODELING NETWORKS OF INHIBITORY NEURONS

Eleonora Catsigeras$^1$, Álvaro Rovella$^2$, Ruben Budelli$^3$
$^1$Institute of Mathematics
Faculty of Engineering
Universidad de la República
565, Julio Herrera y Reissig, Montevideo, 11300, URUGUAY
$^1$e-mail: eleonora@fing.edu.uy
$^{2,3}$Mathematics Centre and Biomathematical Department
Faculty of Sciences
Universidad de la República
4225, Iguá, Montevideo, URUGUAY
$^2$e-mail: leva@cmat.edu.uy
$^3$e-mail: ruben@biomat.fcien.edu.uy


Abstract.We study theoretically the dynamical system of a network composed by a large number of inhibitory pacemaker neurons, evolving deterministically in real time with a relatively large dissipation rate. We consider the first return map $F$ to a Poincaré section of the phase space and prove that it is piecewise continuous, locally contractive and has the ``separation property": different continuity pieces have disjoint images.

Received: April 15, 2010

AMS Subject Classification: 34C25, 92B20

Key Words and Phrases: piecewise-continuous dynamics, neural networks

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 4