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Volume 5, Issue 1
Dynamical Property Analysis of a Delayed Diffusive Predator-Prey Model with Fear Effect

Xiao Zhao & Ruizhi Yang

DOI: 10.12150/jnma.2023.1

J. Nonl. Mod. Anal., 5 (2023), pp. 1-23.

Published online: 2023-08

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

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  • Abstract

In this paper, we study a delayed diffusive predator-prey model with fear effect and Holling II functional response. The stability of the positive equilibrium is investigated. We find that time delay can destabilize the stable equilibrium and induce Hopf bifurcation. Diffusion may lead to Turing instability and inhomogeneous periodic solutions. Through the theory of center manifold and normal form, some detailed formulas for determining the property of Hopf bifurcation are presented. Some numerical simulations are also provided.

  • Keywords

Delay, Diffusion, Predator-prey, Turing instability, Hopf bifurcation.

  • AMS Subject Headings

35B32, 34C23

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-1, author = {Zhao , Xiao and Yang , Ruizhi}, title = {Dynamical Property Analysis of a Delayed Diffusive Predator-Prey Model with Fear Effect}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {1}, pages = {1--23}, abstract = {

In this paper, we study a delayed diffusive predator-prey model with fear effect and Holling II functional response. The stability of the positive equilibrium is investigated. We find that time delay can destabilize the stable equilibrium and induce Hopf bifurcation. Diffusion may lead to Turing instability and inhomogeneous periodic solutions. Through the theory of center manifold and normal form, some detailed formulas for determining the property of Hopf bifurcation are presented. Some numerical simulations are also provided.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.1}, url = {http://global-sci.org/intro/article_detail/jnma/21914.html} }
TY - JOUR T1 - Dynamical Property Analysis of a Delayed Diffusive Predator-Prey Model with Fear Effect AU - Zhao , Xiao AU - Yang , Ruizhi JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 1 EP - 23 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.1 UR - https://global-sci.org/intro/article_detail/jnma/21914.html KW - Delay, Diffusion, Predator-prey, Turing instability, Hopf bifurcation. AB -

In this paper, we study a delayed diffusive predator-prey model with fear effect and Holling II functional response. The stability of the positive equilibrium is investigated. We find that time delay can destabilize the stable equilibrium and induce Hopf bifurcation. Diffusion may lead to Turing instability and inhomogeneous periodic solutions. Through the theory of center manifold and normal form, some detailed formulas for determining the property of Hopf bifurcation are presented. Some numerical simulations are also provided.

Xiao Zhao & Ruizhi Yang. (2023). Dynamical Property Analysis of a Delayed Diffusive Predator-Prey Model with Fear Effect. Journal of Nonlinear Modeling and Analysis. 5 (1). 1-23. doi:10.12150/jnma.2023.1
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