IJPAM: Volume 61, No. 4 (2010)
CONTRACTIVE PIECEWISE CONTINUOUS MAPS
MODELING NETWORKS OF INHIBITORY NEURONS
MODELING NETWORKS OF INHIBITORY NEURONS
Eleonora Catsigeras
, Álvaro Rovella
, Ruben Budelli
Institute of Mathematics
Faculty of Engineering
Universidad de la República
565, Julio Herrera y Reissig, Montevideo, 11300, URUGUAY
e-mail: [email protected]
Mathematics Centre and Biomathematical Department
Faculty of Sciences
Universidad de la República
4225, Iguá, Montevideo, URUGUAY
e-mail: [email protected]
e-mail: [email protected]
, Álvaro Rovella, Ruben Budelli
Institute of Mathematics
Faculty of Engineering
Universidad de la República
565, Julio Herrera y Reissig, Montevideo, 11300, URUGUAY
e-mail: [email protected]
Mathematics Centre and Biomathematical Department
Faculty of Sciences
Universidad de la República
4225, Iguá, Montevideo, URUGUAY
e-mail: [email protected]
e-mail: [email protected]
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 
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