Stability switches and Hopf bifurcation in a coupled FitzHugh-Nagumo neural system with multiple delays
type: Item
instance of: scholarly article
title: Stability switches and Hopf bifurcation in a coupled FitzHugh-Nagumo neural system with multiple delays
zbMATH Open document ID: 1474.34488
DOI: 10.1155/2014/874701
author: Shengwei Yao
author: Huonian Tu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A FitzHugh-Nagumo (FHN) neural system with multiple delays has been proposed. The number of equilibrium point is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the saddle-node bifurcation of nontrivial equilibrium point and transcritical bifurcation of trivial one. Further, the stability of equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving the multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independence and delay-dependence stability. Increasing delay induces the stability switching between resting state and periodic activity in some parameter regions of coupling weight. Finally, numerical simulations are taken to support the theoretical results.
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 92C20
zbMATH DE Number: 7023237
Wikidata QID: Q59042223
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/874701
OpenAlex ID: W2106441681
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description: scientific article; zbMATH DE number 7023237