Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee EffectReport as inadecuate




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Journal of Applied MathematicsVolume 2013 2013, Article ID 535746, 16 pages

Research Article

School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China

College 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.

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 thestability 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 andalso to stripes. These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity.





Author: Yongli Cai, Caidi Zhao, and Weiming Wang

Source: https://www.hindawi.com/



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