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- N. Romero, A. Rovella, F. Vilamajó
- Appl. Math. Lett.
- 2006

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)

Consider a continuous surjective self map of the open annulus with degree d > 1. It is proved that the number of Nielsen classes of periodic points is maximum possible whenever f has a completely invariant essential continuum. The same result is obtained in negative degree |d| > 1 and for just forward invariant essential continua, provided that the… (More)

In this article we classify the set of geometrically stable quadratic mappings of the plane, characterizing its set of critical points and critical values. We also complete the proof given in [2] of the fact that generic quadratic maps of the plane without fixed points have a Lyapunov function and hence empty limit set.

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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