Exponential Period of Neuronal Recurrence Automata with Excitatory Memory by René Ndoundam and Maurice Tchuente

Exponential Period of Neuronal Recurrence Automata with Excitatory Memory

René Ndoundam
Electronic mail address: ndoundam@uycdc.uninet.cm.

Maurice Tchuente
Electronic mail address: tchuente@camnet.cm.
Department of Computer Science,
Faculty of Science, University of Yaounde I,
P.O. Box 812 Yaounde, Cameroon

Abstract

The sequences generated by a neuronal recurrence equation with memory of the form $x (n) = 1 [\sum_{i = 1}^{h} a_{i} x (n - i) - θ]$ , where h is the size of the memory, are studied. It is shown that in the case where all the parameters ${(a_{i})}_{1 \leq i \leq h}$ are positive reals, there exists a neuronal recurrence equation of memory length h that generates a sequence of period $Ω (e^{\sqrt[3]{{h (\ln (h))}^{2}}})$ . This result shows that in the case where all the weighting coefficients are positive reals, the neuronal recurrence equation exhibits a complex behavior.

https://doi.org/10.25088/ComplexSystems.15.1.79