Multiple nonlinear oscillations in a \(\mathbb D_3\times\mathbb D_3\)-symmetrical coupled system of identical cells with delays
type: Item
instance of: scholarly article
title: Multiple nonlinear oscillations in a \(\mathbb D_3\times\mathbb D_3\)-symmetrical coupled system of identical cells with delays
zbMATH Open document ID: 1342.34092
DOI: 10.1155/2013/417678
author: Haijun Hu
author: Li Liu
author: Jie Mao
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: A coupled system of nine identical cells with delays and \(\mathbb D_3\times\mathbb D_3\)-symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 37G40
zbMATH DE Number: 6306819
zbMATH Keywords: nonlinear delayed feedback
zbMATH Keywords: characteristic equations
zbMATH Keywords: linear stability
zbMATH Keywords: multiple periodic solutions
Wikidata QID: Q58916237
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/417678
OpenAlex ID: W2084117002
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description: scientific article; zbMATH DE number 6306819