We stu dy t he dyn ami cs of an automaton wit h me mory whose equation is t he following: '-1 Xntl = lC L: a j Xn _ l - 0) i =O wher e a = (ai)i=o...k _ l deno tes t he cou pling coefficients vector. We show that if a is symmetric, t hen wecan introduce an energy operator; t hereby we slate that the periods of t he a utomaton always divide (k + 1) and give a bound of t he t ra nsient . We also st udy t he case of reversible syste ms a nd cha racte rize reversibili ty versus t he coupling coeffici ents . T hereafter, we give some result s about t he pivot sums syste ms. Some conject ures concern ing the general case are given.
['Michel Cosnard', 'Dris Moumida', 'Eric Goles', 'Thierry de St. Pierre']
Dynamical behavior of a neural automaton with memory