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.
Publisher
Vilnius Gediminas Technical University
Subject
Modeling and Simulation,Analysis
Cited by
6 articles.
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1. Chaotic single neuron model with periodic coefficients with period two;Nonlinear Analysis: Modelling and Control;2023-12-13
2. Behaviour of Solutions of a Neuron Model;13th Chaotic Modeling and Simulation International Conference;2021
3. Eventually periodic solutions of single neuron model;Nonlinear Analysis: Modelling and Control;2020-11-01
4. Periodic Character of Solutions of First Order Nonlinear Difference Equations;Periodic Character and Patterns of Recursive Sequences;2018
5. Neuron model with a period three internal decay rate;Electronic Journal of Qualitative Theory of Differential Equations;2017