# American Institute of Mathematical Sciences

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2016, 13(3): 597-611. doi: 10.3934/mbe.2016010

## A new firing paradigm for integrate and fire stochastic neuronal models

 1 Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123 Torino 2 Department of Mathematics G. Peano, University of Torino, Via Carlo Alberto 10, 10123 - Torino, Italy

Received  May 2015 Revised  October 2015 Published  January 2016

A new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved.
Citation: Roberta Sirovich, Luisa Testa. A new firing paradigm for integrate and fire stochastic neuronal models. Mathematical Biosciences & Engineering, 2016, 13 (3) : 597-611. doi: 10.3934/mbe.2016010
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