A note on a neuron network model with diffusion

Philippe Michel; Suman Kumar Tumuluri

doi:10.3934/dcdsb.2020085

Article Contents

2020, Volume 25, Issue 9: 3659-3676. Doi: 10.3934/dcdsb.2020085

This issue Previous Article Stability of delay differential equations with fading stochastic perturbations of the type of white noise and poisson's jumps Next Article From approximate synchronization to identical synchronization in coupled systems

A note on a neuron network model with diffusion

Philippe Michel^1, and
Suman Kumar Tumuluri^2, ,

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
^* Corresponding author: Suman Kumar Tumuluri

Received: January 2019

Revised: November 2019

Early access: April 2020

Published: September 2020

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Abstract

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.

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Mathematics Subject Classification: Primary: 35A01, 35A02, 35K20, 35K55, 92D25.

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References

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