United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS METHOD OF CONSTRUCTION OF TRANSIENT FROM A CYCLE OF NEURONAL RECURRENCE EQUATION

We study the sequences generated by neuronal recurrence equations of the form x(n) = 1[ ∑k j=1 ajx(n − j) − θ], where k is the size of memory (k represents the number of previous states x(n − 1), x(n − 2), . . . , x(n − k) which intervene in the calculation of x(n)). We are interested in the number of steps (transient length) from an initial configuration to the cycle. We propose a method of construction of transient from a cycle generated by neuronal recurrence equation. We apply this method to build a neuronal recurrence equation with inhibitory memory of size (s+1)6m, whose dynamics contains an evolution of transient length (s+1)× (5m+2+ lcm(p0, p1, . . . , ps−1, 3m − 1)) and a cycle of length (s + 1) × lcm(p0, p1, . . . , ps−1, 2m + 1) where lcm denotes the least common multiple, and p0, p1, . . . , ps−1 are prime numbers lying between 2m and 3m. MIRAMARE – TRIESTE November 2005 Regular Associate of ICTP.