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Volume 7, Issue 2
Dynamics of an $n$-Patch Predator-Prey Model with Allee Effect

Zhaolei Zhu, Zhichun Yang & Weisong Zhou

DOI: 10.12150/jnma.2025.414

J. Nonl. Mod. Anal., 7 (2025), pp. 414-428.

Published online: 2025-04

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

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  • Abstract

A class of $n$-patch predator-prey diffusion models with the Allee effect is established. The influence of the Allee effect and diffusion of prey on the existence and stability of the equilibrium point are investigated. Firstly, sufficient conditions for the permanence and extinction of the system are analyzed. Secondly, by constructing a new Lyapunov function in terms of graph theory, we obtain a sufficient condition of the global asymptotical stability for the positive equilibrium point. Finally, our results of this paper are verified by Matlab simulation.

  • Keywords

$n$-patch, stability, Allee effect, predation-prey model.

  • AMS Subject Headings

34A12, 34D23

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-414, author = {Zhu , ZhaoleiYang , Zhichun and Zhou , Weisong}, title = {Dynamics of an $n$-Patch Predator-Prey Model with Allee Effect}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {2}, pages = {414--428}, abstract = {

A class of $n$-patch predator-prey diffusion models with the Allee effect is established. The influence of the Allee effect and diffusion of prey on the existence and stability of the equilibrium point are investigated. Firstly, sufficient conditions for the permanence and extinction of the system are analyzed. Secondly, by constructing a new Lyapunov function in terms of graph theory, we obtain a sufficient condition of the global asymptotical stability for the positive equilibrium point. Finally, our results of this paper are verified by Matlab simulation.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.414}, url = {http://global-sci.org/intro/article_detail/jnma/23981.html} }
TY - JOUR T1 - Dynamics of an $n$-Patch Predator-Prey Model with Allee Effect AU - Zhu , Zhaolei AU - Yang , Zhichun AU - Zhou , Weisong JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 414 EP - 428 PY - 2025 DA - 2025/04 SN - 7 DO - http://doi.org/10.12150/jnma.2025.414 UR - https://global-sci.org/intro/article_detail/jnma/23981.html KW - $n$-patch, stability, Allee effect, predation-prey model. AB -

A class of $n$-patch predator-prey diffusion models with the Allee effect is established. The influence of the Allee effect and diffusion of prey on the existence and stability of the equilibrium point are investigated. Firstly, sufficient conditions for the permanence and extinction of the system are analyzed. Secondly, by constructing a new Lyapunov function in terms of graph theory, we obtain a sufficient condition of the global asymptotical stability for the positive equilibrium point. Finally, our results of this paper are verified by Matlab simulation.

Zhu , ZhaoleiYang , Zhichun and Zhou , Weisong. (2025). Dynamics of an $n$-Patch Predator-Prey Model with Allee Effect. Journal of Nonlinear Modeling and Analysis. 7 (2). 414-428. doi:10.12150/jnma.2025.414
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