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.
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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