No Polynomial Bound for the Period of Neuronal Automata with Inhibitory Memory.

Abstract

We study the sequences generated by a neuronal equation with memory of the form xn = 1 [ Pk i=1 aixn−i−θ], where k is the size of the memory. We show that in the case where all the parameters (ai)1≤i≤k are negative real numbers, there exists a neuronal equation of memory length k that generates a sequence of period e Ω( √ klogk). This result shows that in the case where all weighting coefficients are negative, the neuronal recurrence equation exhibits a complex behavior. 1