Hu, Guangping; Li, Xiaoling Stationary patterns of a Leslie-Gower-type three-species model with cross-diffusions. (Chinese. English summary) Zbl 1289.92042 Acta Math. Sci., Ser. A, Chin. Ed. 33, No. 1, 16-27 (2013). Summary: This paper is concerned with a Leslie-Gower-type three-species model subject to the homogeneous Neumann boundary condition. We show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can occur due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create stationary patterns. MSC: 92D25 Population dynamics (general) 35Q92 PDEs in connection with biology, chemistry and other natural sciences 35J48 Higher-order elliptic systems 92D40 Ecology Keywords:cross-diffusion; a predator-prey system; priori estimates; non-constant positive steady state PDFBibTeX XMLCite \textit{G. Hu} and \textit{X. Li}, Acta Math. Sci., Ser. A, Chin. Ed. 33, No. 1, 16--27 (2013; Zbl 1289.92042)