## Period-Halving Bifurcation of a Neuronal Recurrence Equation

**René Ndoundam***University of Yaounde I, UMI 209, UMMISCO**P.O. Box 337 Yaounde, Cameroon**and**University of Yaounde I, LIRIMA**Team GRIMCAPE, Faculty of Science, Department of Computer Science**P.O. Box 812 Yaounde, Cameroon**ndoundam@gmail.com*

#### Abstract

The sequences generated by neuronal recurrence equations of the form are studied. From a neuronal recurrence equation of memory size h that describes a cycle of length , a set of neuronal recurrence equations is constructed with dynamics that describe respectively the transient of length and the cycle of length if and 1 if . This result shows the exponential time of the convergence of the neuronal recurrence equation to fixed points and the existence of the period-halving bifurcation.