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Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model

Author

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  • Xinze Lian
  • Yanhong Yue
  • Hailing Wang

Abstract

This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with self- and cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spots, stripes, and spiral wave pattern replication, which show that reaction-diffusion model is useful to reveal the spatial predation dynamics in the real world.

Suggested Citation

  • Xinze Lian & Yanhong Yue & Hailing Wang, 2012. "Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, November.
    • Handle: RePEc:hin:jnddns:814069
    DOI: 10.1155/2012/814069
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    Cited by:

    1. Meng Zhu & Jing Li & Xinze Lian, 2022. "Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation," Mathematics, MDPI, vol. 10(17), pages 1-20, September.

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