Contractive piecewise continuous maps modeling networks of inhibitory neurons

Details Contractive piecewise continuous maps modeling networks of inhibitory neurons Contractive piecewise continuous maps modeling networks of inhibitory neurons

2008-05-17

arxiv.org/abs/0805.2695v2

International Journal of Pure and Applied Mathematics, Volume 61 Number 4 2010, 381-407

Mathematics

Dynamical Systems

In this version we changed the section 2 to include a complete proof of the properties of the mathematical model from a physic

Scientific paper

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 Poincare 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.

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