Abstract
We investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions. Some results of solutions to this model and its corresponding steady-state problem are shown. More precisely, we give the stability of the positive constant steady-state solution, the refined a priori estimates of positive solution, and the nonexistence and existence of the positive nonconstant solutions. We carry out the analytical study for two-dimensional system in detail and find out the certain conditions for Turing instability. Furthermore, we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and also to stripes. These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity.
Citation
Yongli Cai. Caidi Zhao. Weiming Wang. "Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect." J. Appl. Math. 2013 1 - 16, 2013. https://doi.org/10.1155/2013/535746