Global Hopf bifurcation analysis for an avian influenza virus propagation model with nonlinear incidence rate and delay
type: Item
instance of: scholarly article
title: Global Hopf bifurcation analysis for an avian influenza virus propagation model with nonlinear incidence rate and delay
zbMATH Open document ID: 1406.92639
DOI: 10.1155/2014/242410
author: Ying Xiong
author: Xiaona Ma
author: Haiyun Bai
author: Yanhui Zhai
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7021984
zbMATH Keywords: avian influenza virus propagation
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: nonlinear incidence rate
zbMATH Keywords: periodic solution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/242410
OpenAlex ID: W2066720859
Wikidata QID: Q59036690
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description: scientific article; zbMATH DE number 7021984