Periodic and Chaotic Orbits of a Neuron Model

Abstract

In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.

Keywords:

• chaotic mapping
• dynamical system
• iterative process
• nonlinear problem
• stability

AMS Subject Classification:

• 39A10
• 39A23
• 92B20