A. Rovella

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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(More)
In this paper we develop some techniques to obtain global hyperbolicity for a certain class of endomorphisms of (R) with p, n ≥ 2. This kind of endomorphisms are obtained from vectorial difference equations where the mapping defining these equations satisfy a circulant condition. In particular, we show that one-parameter families of these quadratic(More)
In this paper we develop some techniques to obtain global hyperbolicity for a certain class of endomorphisms of Rn called real cellular automata, which are characterized by the property of commuting with a shift. In particular, we show that one parameter families of generic quadratic cellular automata in Rn are hyperbolic for large values of the parameter.
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