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Turing Patterns in a Predator‐Prey System with Self‐Diffusion

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  • Hongwei Yin
  • Xiaoyong Xiao
  • Xiaoqing Wen

Abstract

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.

Suggested Citation

  • Hongwei Yin & Xiaoyong Xiao & Xiaoqing Wen, 2013. "Turing Patterns in a Predator‐Prey System with Self‐Diffusion," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:891738
    DOI: 10.1155/2013/891738
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    References listed on IDEAS

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    1. Xue, Lin, 2012. "Pattern formation in a predator–prey model with spatial effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5987-5996.
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