Study of all the periods of a Neuronal Recurrence Equation

TL;DR

This paper analyzes the periodic behavior of neuronal recurrence equations, providing a detailed characterization of cycle periods and their bifurcations, which enhances understanding of neural network dynamics.

Contribution

It introduces a comprehensive characterization of cycle periods in neuronal recurrence equations and links these to bifurcation phenomena, advancing theoretical understanding.

Findings

Characterization of k-chains in 0-1 periodic sequences

Description of periods of all cycles in certain neuronal recurrence equations

Demonstration of generalized period-halving bifurcation

Abstract

We characterize the structure of the periods of a neuronal recurrence equation. Firstly, we give a characterization of k-chains in 0-1 periodic sequences. Secondly, we characterize the periods of all cycles of some neuronal recurrence equation. Thirdly, we explain how these results can be used to deduce the existence of the generalized period-halving bifurcation.