Discontinuity-induced dynamics in the Conductance-Based Adaptive Exponential Integrate-and-Fire Model - Inria - Institut national de recherche en sciences et technologies du numérique
Pré-Publication, Document De Travail Année : 2024

Discontinuity-induced dynamics in the Conductance-Based Adaptive Exponential Integrate-and-Fire Model

Résumé

In this article, we present a computational study of the Conductance-Based Adaptive Exponential (CAdEx) integrate-and-fire neuronal model, focusing on its multiple timescale nature, and on how it shapes its main dynamical regimes. In particular, we show that the spiking and so-called delayed bursting regimes of the model are triggered by discontinuity-induced bifurcations that are directly related to the multiple-timescale aspect of the model, and are mediated by canard solutions. By means of a numerical bifurcation analysis of the model, using the software package coco, we can precisely describe the mechanisms behind these dynamical scenarios. Spike-increment transitions are revealed. These transitions are accompanied by a fold and a period-doubling bifurcation, and are organised in parameter space along an isola periodic solutions with resets. Finally, we also unveil the presence of a homoclinic bifurcation terminating a canard explosion which, together with the presence of resets, organises the delayed bursting regime of the model.
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Dates et versions

hal-04665937 , version 1 (01-08-2024)
hal-04665937 , version 2 (10-08-2024)

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  • HAL Id : hal-04665937 , version 2

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Mathieu Desroches, Piotr Kowalczyk, Serafim Rodrigues. Discontinuity-induced dynamics in the Conductance-Based Adaptive Exponential Integrate-and-Fire Model. 2024. ⟨hal-04665937v2⟩
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