Stationary patterns of a ratio-dependent predator-prey system with cross-diffusion

    Yu-Xia Wang Info
    Wan-Tong Li Info
    Hong-Bo Shi Info

Abstract

This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We establish the existence and non-existence of non-constant positive steady states (patterns). In particular, we show that under certain hypotheses, the cross-diffusion can create stationary patterns even though the corresponding model without cross-diffusion fails.

Keywords:

existence, predator-prey system, cross-diffusion, positive steady state, ratiodependence

How to Cite

Wang, Y.-X., Li, W.-T., & Shi, H.-B. (2011). Stationary patterns of a ratio-dependent predator-prey system with cross-diffusion. Mathematical Modelling and Analysis, 16(3), 461-474. https://doi.org/10.3846/13926292.2011.603164

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August 24, 2011
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2011-08-24

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How to Cite

Wang, Y.-X., Li, W.-T., & Shi, H.-B. (2011). Stationary patterns of a ratio-dependent predator-prey system with cross-diffusion. Mathematical Modelling and Analysis, 16(3), 461-474. https://doi.org/10.3846/13926292.2011.603164

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