Stability of stochastic semigroups and applications to Stein's neuronal model

Katarzyna PichÓr; Ryszard Rudnicki

doi:10.3934/dcdsb.2018026

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2018, Volume 23, Issue 1: 377-385. Doi: 10.3934/dcdsb.2018026 open access

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Stability of stochastic semigroups and applications to Stein's neuronal model

Katarzyna PichÓr^1, and
Ryszard Rudnicki^2, ,

1.
Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
2.
Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland

* Corresponding author: Ryszard Rudnicki
* Corresponding author: Ryszard Rudnicki

Received: October 2016

Revised: December 2016

Published: November 2017

This research was partially supported by the National Science Centre (Poland) Grant No. 2014/13/B/ST1/00224.

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Abstract

A new theorem on asymptotic stability of stochastic semigroups is given. This theorem is applied to a stochastic semigroup corresponding to Stein's neuronal model. Asymptotic properties of models with and without the refractory period are compared.

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Mathematics Subject Classification: Primary: 47D06; Secondary: 60J75, 92C20.

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Figure 1. A schematic diagram of the model

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References

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