Open Access
2013 Turing Patterns in a Predator-Prey System with Self-Diffusion
Hongwei Yin, Xiaoyong Xiao, Xiaoqing Wen
Abstr. Appl. Anal. 2013(SI10): 1-10 (2013). DOI: 10.1155/2013/891738


For a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing instability for a predator-prey system with nonlinear diffusion terms including the normal diffusion, cross-diffusion, and self-diffusion. A sufficient condition of Turing instability for this system is obtained by analyzing the linear stability of spatial homogeneous equilibrium state of this model. A series of numerical simulations reveal Turing parameter regions of the interaction of diffusion parameters. According to these regions, we further demonstrate dispersion relations and spatial patterns. Our results indicate that self-diffusion plays an important role in the spatial patterns.


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Hongwei Yin. Xiaoyong Xiao. Xiaoqing Wen. "Turing Patterns in a Predator-Prey System with Self-Diffusion." Abstr. Appl. Anal. 2013 (SI10) 1 - 10, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095463
MathSciNet: MR3126804
Digital Object Identifier: 10.1155/2013/891738

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI10 • 2013
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