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Pattern formation in a predator–prey model with spatial effect

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  • Xue, Lin

Abstract

In this paper, spatial dynamics in the Beddington–DeAngelis predator–prey model with self-diffusion and cross-diffusion is investigated. We analyze the linear stability and obtain the condition of Turing instability of this model. Moreover, we deduce the amplitude equations and determine the stability of different patterns. Numerical simulations show that this system exhibits complex dynamical behaviors. In the Turing space, we find three types of typical patterns. One is the coexistence of hexagon patterns and stripe patterns. The other two are hexagon patterns of different types. The obtained results well enrich the finding in predator–prey models with Beddington–DeAngelis functional response.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:5987-5996
    DOI: 10.1016/j.physa.2012.06.029
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    1. Gui-Quan Sun & Zhen Jin & Yi-Guo Zhao & Quan-Xing Liu & Li Li, 2009. "Spatial Pattern In A Predator-Prey System With Both Self- And Cross-Diffusion," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 71-84.
    2. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
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