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Hopf bifurcation analysis for a model of plant virus propagation with two delays

Authors
  • Li, Qinglian1
  • Dai, Yunxian1
  • Guo, Xingwei1
  • Zhang, Xingyong1, 2
  • 1 Kunming University of Science and Technology, Department of Applied Mathematics, Kunming, People’s Republic of China , Kunming (China)
  • 2 Central South University, School of Mathematics and Statistics, Changsha, People’s Republic of China , Changsha (China)
Type
Published Article
Journal
Advances in Difference Equations
Publisher
Springer International Publishing
Publication Date
Jul 27, 2018
Volume
2018
Issue
1
Identifiers
DOI: 10.1186/s13662-018-1714-8
Source
Springer Nature
Keywords
License
Green

Abstract

In this paper, we consider a model of plant virus propagation with two delays and Holling type II functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are analyzed by choosing τ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau_{1}$\end{document} and τ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\tau_{2}$\end{document} as bifurcation parameters, respectively. Using the center manifold theory and normal form method, we discuss conditions for determining the stability and the bifurcation direction of the bifurcating periodic solution. Finally, we carry out numerical simulations to illustrate the theoretical analysis.

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