SEQUENCES GENERATED BY A NEURONAL RECURRE NCE EQUATION WITH MEMORY

In this paper, we study the sequences generated by neuronal recurrence equations of the form x(n)= 1 (SIGMA(1 less-than-or-equal-to i less-t han-or-equal-to k) a(i)x(n-i)-theta), where (a(i))1 less-than-or-equal -to i less-than-or-equal-to k and theta are real parameters, and k is a positive integer representing the memory length. It was shown recent ly that, if there is a neuronal recurrence equation with memory length k that generates sequences of periods p0, p1, ..., p(r-1), then there is a neuronal recurrence equation with memory length kr which generat es a sequence of period rlcm (p0, p1, ..., p(r-1)), where lcm denotes the least common multiple. Using this result. we exhibit here a famil y of neuronal recurrence equations which generate sequences of periods e(O(square-root k)), where k is the memory length.