Mathematical Biosciences and Engineering, 2016, 13(3): 483-493. doi: 10.3934/mbe.2016002.

Primary: 60J60; Secondary: 60H35.

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A leaky integrate-and-fire model with adaptation for the generation of a spike train

1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli
2. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli
3. Istituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, Napoli

A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described.
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Keywords hazard rate method.; Calcium-activated potassium current; fast-slow analysis

Citation: Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. A leaky integrate-and-fire model with adaptation for the generation of a spike train. Mathematical Biosciences and Engineering, 2016, 13(3): 483-493. doi: 10.3934/mbe.2016002

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