# Long time behavior of an age and leaky memory-structured neuronal population equation

@inproceedings{Fonte2021LongTB, title={Long time behavior of an age and leaky memory-structured neuronal population equation}, author={Claudia Fonte and Valentin Schmutz}, year={2021} }

We study the asymptotic stability of a two-dimensional mean-field equation, which takes the form of a nonlocal transport equation and generalizes the time-elapsed neuron network model by the inclusion of a leaky memory variable. This additional variable can represent a slow fatigue mechanism, like spike frequency adaptation or short-term synaptic depression. Even though two-dimensional models are known to have emergent behaviors, like population bursts, which are not observed in standard one…

## 2 Citations

A multiple time renewal equation for neural assemblies with elapsed time model

- Mathematics
- 2021

An extension of the classical elapsed time equation is introduced and study in the context of neuron populations that are described by the elapsed time since the last discharge, i.e., the refractory period, and a more complex system of integro-differential equations is obtained.

Mean-field limit of age and leaky memory dependent Hawkes processes

- Computer Science, BiologyStochastic Processes and their Applications
- 2022

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