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

  • * Corresponding author: Ryszard Rudnicki

    * Corresponding author: Ryszard Rudnicki

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

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  • 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.

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

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  • Figure 1.  A schematic diagram of the model

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