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Periodic and Chaotic Orbits of a Neuron Model

    Aija Anisimova Affiliation
    ; Maruta Avotina Affiliation
    ; Inese Bula Affiliation

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.

Keyword : chaotic mapping, dynamical system, iterative process, nonlinear problem, stability

How to Cite
Anisimova, A., Avotina, M., & Bula, I. (2015). Periodic and Chaotic Orbits of a Neuron Model. Mathematical Modelling and Analysis, 20(1), 30-52. https://doi.org/10.3846/13926292.2015.1000411
Published in Issue
Feb 3, 2015
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This work is licensed under a Creative Commons Attribution 4.0 International License.