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Volume 3, Issue 3
Hopf Bifurcation Analysis of a Host-Generalist Parasitoid Model with Diffusion Term and Time Delay

Zijun Liu & Ruizhi Yang

DOI: 10.12150/jnma.2021.447

J. Nonl. Mod. Anal., 3 (2021), pp. 447-463.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we studied a delayed host-generalist parasitoid model with Holling II functional response and diffusion term. The Turing instability and local stability are studied. The existence of Hopf bifurcation is investigated, and some explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of center manifold and normal form method. Some numerical simulations are carried out.

  • Keywords

Delay, Diffusion, Turing instability, Hopf bifurcation.

  • AMS Subject Headings

34K18, 35B32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-3-447, author = {Liu , Zijun and Yang , Ruizhi}, title = {Hopf Bifurcation Analysis of a Host-Generalist Parasitoid Model with Diffusion Term and Time Delay}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {3}, number = {3}, pages = {447--463}, abstract = {

In this paper, we studied a delayed host-generalist parasitoid model with Holling II functional response and diffusion term. The Turing instability and local stability are studied. The existence of Hopf bifurcation is investigated, and some explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of center manifold and normal form method. Some numerical simulations are carried out.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2021.447}, url = {http://global-sci.org/intro/article_detail/jnma/20677.html} }
TY - JOUR T1 - Hopf Bifurcation Analysis of a Host-Generalist Parasitoid Model with Diffusion Term and Time Delay AU - Liu , Zijun AU - Yang , Ruizhi JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 447 EP - 463 PY - 2022 DA - 2022/06 SN - 3 DO - http://doi.org/10.12150/jnma.2021.447 UR - https://global-sci.org/intro/article_detail/jnma/20677.html KW - Delay, Diffusion, Turing instability, Hopf bifurcation. AB -

In this paper, we studied a delayed host-generalist parasitoid model with Holling II functional response and diffusion term. The Turing instability and local stability are studied. The existence of Hopf bifurcation is investigated, and some explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of center manifold and normal form method. Some numerical simulations are carried out.

Zijun Liu & Ruizhi Yang. (2022). Hopf Bifurcation Analysis of a Host-Generalist Parasitoid Model with Diffusion Term and Time Delay. Journal of Nonlinear Modeling and Analysis. 3 (3). 447-463. doi:10.12150/jnma.2021.447
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