Volume 3, Issue 2
Stability Analysis of a Diffusive Predator-Prey Model with Hunting Cooperation

Shuhao Wu & Yongli Song

J. Nonl. Mod. Anal., 3 (2021), pp. 321-334.

Published online: 2021-04

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

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  • Abstract

In this paper, we are concerned with the dynamics of a diffusive predator-prey model that incorporates the functional response concerning hunting cooperation. First, we investigate the stability of the semi-trivial steady state. Then, we investigate the influence of the diffusive rates on the stability of the positive constant steady state. It is shown that there exists diffusion-driven Turing instability when the diffusive rate of the predator is smaller than the critical value, which is dependent on the diffusive rate of the prey, and the semi-trivial steady state and the positive constant steady state are both locally asymptotically stable when the diffusive rate of the predator is larger than the critical value. Finally, the nonexistence of nonconstant steady states is discussed.

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@Article{JNMA-3-321, author = {Wu , Shuhao and Song , Yongli}, title = {Stability Analysis of a Diffusive Predator-Prey Model with Hunting Cooperation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {3}, number = {2}, pages = {321--334}, abstract = {

In this paper, we are concerned with the dynamics of a diffusive predator-prey model that incorporates the functional response concerning hunting cooperation. First, we investigate the stability of the semi-trivial steady state. Then, we investigate the influence of the diffusive rates on the stability of the positive constant steady state. It is shown that there exists diffusion-driven Turing instability when the diffusive rate of the predator is smaller than the critical value, which is dependent on the diffusive rate of the prey, and the semi-trivial steady state and the positive constant steady state are both locally asymptotically stable when the diffusive rate of the predator is larger than the critical value. Finally, the nonexistence of nonconstant steady states is discussed.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2021.321}, url = {http://global-sci.org/intro/article_detail/jnma/18793.html} }
TY - JOUR T1 - Stability Analysis of a Diffusive Predator-Prey Model with Hunting Cooperation AU - Wu , Shuhao AU - Song , Yongli JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 321 EP - 334 PY - 2021 DA - 2021/04 SN - 3 DO - http://doi.org/10.12150/jnma.2021.321 UR - https://global-sci.org/intro/article_detail/jnma/18793.html KW - Predator-prey model, Hunting cooperation, Stability, Turing bifurcation. AB -

In this paper, we are concerned with the dynamics of a diffusive predator-prey model that incorporates the functional response concerning hunting cooperation. First, we investigate the stability of the semi-trivial steady state. Then, we investigate the influence of the diffusive rates on the stability of the positive constant steady state. It is shown that there exists diffusion-driven Turing instability when the diffusive rate of the predator is smaller than the critical value, which is dependent on the diffusive rate of the prey, and the semi-trivial steady state and the positive constant steady state are both locally asymptotically stable when the diffusive rate of the predator is larger than the critical value. Finally, the nonexistence of nonconstant steady states is discussed.

Wu , Shuhao and Song , Yongli. (2021). Stability Analysis of a Diffusive Predator-Prey Model with Hunting Cooperation. Journal of Nonlinear Modeling and Analysis. 3 (2). 321-334. doi:10.12150/jnma.2021.321
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