## Cyclic Evolution of Neuronal Automata with Memory When All the Weighting Coefficients are Strictly Positive

**René Ndoundam***Electronic mail address: ndoundam@uycdc.uninet.cm.**Département d'Informatique,**Faculté des Sciences,**Université de Yaoundé I,**B.P 812 Yaoundé, Cameroun*

**Martín Matamala***Electronic mail address: mmatamal@dim.uchile.cl.**Departamento de Ingeniería Matemática,**Universidad de Chile,**Casilla 170-correo 3, Santiago, Chile*

#### Abstract

In this paper we study the sequences generated by a neuronal equation of the form , where is the size of the memory. We show that in the case where all the parameters are strictly positive reals and is a multiple of 6 (i.e., ), there exists a subset of and for which there exists a neuronal equation of memory length (i.e., ) with strictly positive weighting coefficients that generates a sequence of period . As an application; first, for all integer greater than or equal to 3, we exhibit a neuronal recurrence equation of memory length with weighting coefficients that are all strictly positive and which generates a sequence of period ; and second, for all odd integer greater than or equal to 5, we exhibit a neuronal equation of memory length with strictly positive weighting coefficients that generates a sequence of period .