Volume 2, Issue 2
Spatial Dynamics of a Diffusive Predator-Prey Model with Leslie-Gower Functional Response and Strong Allee Effect

Fengru Wei, Cuihua Wang & Sanling Yuan

J. Nonl. Mod. Anal., 2 (2020), pp. 267-285.

Published online: 2021-04

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In this paper, spatial dynamics of a diffusive predator-prey model with Leslie-Gower functional response and strong Allee effect is studied. Firstly, we obtain the critical condition of Hopf bifurcation and Turing bifurcation of the PDE model. Secondly, taking self-diffusion coefficient of the prey as bifurcation parameter, the amplitude equations are derived by using multi-scale analysis methods. Finally, numerical simulations are carried out to verify our theoretical results. The simulations show that with the decrease of self-diffusion coefficient of the prey, the preys present three pattern structures: spot pattern, mixed pattern, and stripe pattern. We also observe the transition from spot patterns to stripe patterns of the prey by changing the intrinsic growth rate of the predator. Our results reveal that both diffusion and the intrinsic growth rate play important roles in the spatial distribution of species.

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@Article{JNMA-2-267, author = {Wei , FengruWang , Cuihua and Yuan , Sanling}, title = {Spatial Dynamics of a Diffusive Predator-Prey Model with Leslie-Gower Functional Response and Strong Allee Effect}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {2}, number = {2}, pages = {267--285}, abstract = {

In this paper, spatial dynamics of a diffusive predator-prey model with Leslie-Gower functional response and strong Allee effect is studied. Firstly, we obtain the critical condition of Hopf bifurcation and Turing bifurcation of the PDE model. Secondly, taking self-diffusion coefficient of the prey as bifurcation parameter, the amplitude equations are derived by using multi-scale analysis methods. Finally, numerical simulations are carried out to verify our theoretical results. The simulations show that with the decrease of self-diffusion coefficient of the prey, the preys present three pattern structures: spot pattern, mixed pattern, and stripe pattern. We also observe the transition from spot patterns to stripe patterns of the prey by changing the intrinsic growth rate of the predator. Our results reveal that both diffusion and the intrinsic growth rate play important roles in the spatial distribution of species.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.267}, url = {http://global-sci.org/intro/article_detail/jnma/18811.html} }
TY - JOUR T1 - Spatial Dynamics of a Diffusive Predator-Prey Model with Leslie-Gower Functional Response and Strong Allee Effect AU - Wei , Fengru AU - Wang , Cuihua AU - Yuan , Sanling JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 267 EP - 285 PY - 2021 DA - 2021/04 SN - 2 DO - http://doi.org/10.12150/jnma.2020.267 UR - https://global-sci.org/intro/article_detail/jnma/18811.html KW - Predator-prey model, Leslie-Gower functional response, Allee effect, Turing bifurcation, Amplitude equations, Pattern formation. AB -

In this paper, spatial dynamics of a diffusive predator-prey model with Leslie-Gower functional response and strong Allee effect is studied. Firstly, we obtain the critical condition of Hopf bifurcation and Turing bifurcation of the PDE model. Secondly, taking self-diffusion coefficient of the prey as bifurcation parameter, the amplitude equations are derived by using multi-scale analysis methods. Finally, numerical simulations are carried out to verify our theoretical results. The simulations show that with the decrease of self-diffusion coefficient of the prey, the preys present three pattern structures: spot pattern, mixed pattern, and stripe pattern. We also observe the transition from spot patterns to stripe patterns of the prey by changing the intrinsic growth rate of the predator. Our results reveal that both diffusion and the intrinsic growth rate play important roles in the spatial distribution of species.

Wei , FengruWang , Cuihua and Yuan , Sanling. (2021). Spatial Dynamics of a Diffusive Predator-Prey Model with Leslie-Gower Functional Response and Strong Allee Effect. Journal of Nonlinear Modeling and Analysis. 2 (2). 267-285. doi:10.12150/jnma.2020.267
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