Qualitative analysis of a quadratic integrate-and-fire neuron model with state-dependent feedback control
type: Item
instance of: scholarly article
title: Qualitative analysis of a quadratic integrate-and-fire neuron model with state-dependent feedback control
zbMATH Open document ID: 1418.92028
DOI: 10.1155/2015/836402
author: Guangyao Tang
author: Jin Yang
author: Sanyi Tang
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: Spiking neuron models which exhibit rich dynamics are usually defined by hybrid dynamical systems. It is revealed that mathematical analysis of these models has important significance. Therefore, in this work, we provide a comprehensively qualitative analysis for a quadratic integrate-and-fire model by using the theories of hybrid dynamical system. Firstly, the exact impulsive and phase sets are defined according to the phase portraits of the proposed model, and then the Poincaré map is constructed. Furthermore, the conditions for the existence and stability of an order 1 periodic solution are provided. Moreover, the existence and nonexistence of an order \(k\) (\(k \geq 2\)) periodic solution have been studied theoretically and numerically, and the results show that the system has periodic solutions with any period. Finally, some biological implications of the mathematical results are discussed.
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 7025515
Wikidata QID: Q59105493
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/836402
OpenAlex ID: W1856950496
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description: scientific article; zbMATH DE number 7025515