# American Institute of Mathematical Sciences

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September  2020, 25(9): 3659-3676. doi: 10.3934/dcdsb.2020085

## A note on a neuron network model with diffusion

 1 Ecole Centrale de Lyon, University Claude Bernard Lyon 1, CNRS UMR 5208, Ecully, 69130, France 2 School of Mathematics and Statistics, University of Hyderabad, Hyderabad, India

* Corresponding author: Suman Kumar Tumuluri

Received  January 2019 Revised  November 2019 Published  April 2020

We study the dynamics of an inhomogeneous neuronal network parametrized by a real number $\sigma$ and structured by the time elapsed since the last discharge. The dynamics are governed by the parabolic PDE which describes the probability density of neurons with elapsed time $s$ after its last discharge. We prove existence and uniqueness of a solution to the model. Moreover, we show that under some conditions on the connectivity and the firing rate, the network exhibits total desynchronization.

Citation: Philippe Michel, Suman Kumar Tumuluri. A note on a neuron network model with diffusion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3659-3676. doi: 10.3934/dcdsb.2020085
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