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 
.
