Sequential simulation of parallel iterations and applications
Theoretical Computer Science
Lyapunov functions associated to automata networks
Centre National de Recherche Scientifique on Automata networks in computer science: theory and applications
Automata networks and artificial intelligence
Centre National de Recherche Scientifique on Automata networks in computer science: theory and applications
Dynamical behavior of a neural automaton with memory
Complex Systems
Neural and automata networks: dynamical behavior and applications
Neural and automata networks: dynamical behavior and applications
Recursive construction of periodic steady state for neural networks
Theoretical Computer Science
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
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We study the sequences generated by neuronal recurrence equations of the form x(n) = 1[Σj=1k 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, where the length of the cycle represents the period. We show that under certain hypotheses it is possible to build a neuronal recurrence equation of memory size (s + 1)6m, whose dynamics contains an evolution of transient length (s + 1)(3m + 1 + lcm(p0, p1,...,ps-1,3m-1)) and a cycle of length (s + 1) lcm(p0, p1,....,ps-1), where lcm denotes the least common multiple and p0, p1,....,ps-1 are prime numbers lying between 2m and 3m.