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 - <p style="text-align: justify;">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.</p>