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

Yongli Cai, Caidi Zhao and Weiming Wang

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/535746

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:535746

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().