Averaging method for the existence of singular canards in a two-cell inhibitory neural network

¹ Department of Mathematics, Jinan University - Guangzhou 510632, China
² School of Mathematics, South China University of Technology - Guangzhou 510640, China
³ Potsdam Institute for Climate Impact Research - Potsdam 14473, Germany
⁴ Department of Physics, Humboldt University of Berlin - Berlin 12489, Germany

Received: 8 September 2024
Accepted: 8 November 2024

Abstract

Studies of firing rate neuronal competition models, as observed in binocular rivalry, showed that the variation of the stimulus parameters can lead to rich and interesting dynamics. We use the two-cell inhibitory neural network model to address the canards accompanied by the L^s-typed mixed-mode oscillations (MMOs). Specifically, we prove the existence and asymptotic expression of canards for this two-cell model by the average method. Meanwhile, our simulation indicates that the results are in accordance with the theory. Our solution can provide ideas for determining and selecting weights in model fusion of machine learning.