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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 535746, 16 pages
Research Article

Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect

1School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China
2College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

Received 23 April 2013; Revised 27 November 2013; Accepted 28 November 2013

Academic Editor: Victor Kazantsev

Copyright © 2013 Yongli Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.