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Pattern Formation in a Cross-Diffusive Holling-Tanner Model

Author

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  • Weiming Wang
  • Zhengguang Guo
  • R. K. Upadhyay
  • Yezhi Lin

Abstract

We present a theoretical analysis of the processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self- as well as cross-diffusion in a Holling-Tanner predator-prey model; the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained; Hopf and Turing bifurcation in a spatial domain is presented, too. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- as well as cross-diffusion in the model, and find that the model dynamics exhibits a cross-diffusion controlled formation growth not only to spots, but also to strips, holes, and stripes-spots replication. And the methods and results in the present paper may be useful for the research of the pattern formation in the cross-diffusive model.

Suggested Citation

  • Weiming Wang & Zhengguang Guo & R. K. Upadhyay & Yezhi Lin, 2012. "Pattern Formation in a Cross-Diffusive Holling-Tanner Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-12, December.
    • Handle: RePEc:hin:jnddns:828219
    DOI: 10.1155/2012/828219
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