6533b855fe1ef96bd12b083e
RESEARCH PRODUCT
Periodic and Chaotic Orbits of a Neuron Model
Maruta AvotinaAija AnisimovaInese Bulasubject
Discrete mathematicsQuantitative Biology::Neurons and CognitionGeneralizationMathematical analysisChaoticBiological neuron modelFunction (mathematics)stabilityDynamical systemStability (probability)dynamical systemModeling and Simulationiterative processRange (statistics)Orbit (dynamics)QA1-939chaotic mappingnonlinear problemAnalysisMathematicsMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-02-03 | Mathematical Modelling and Analysis |