Peng, Rui; Shi, Junping; Wang, Mingxin Stationary pattern of a ratio-dependent food chain model with diffusion. (English) Zbl 1210.35268 SIAM J. Appl. Math. 67, No. 5, 1479-1503 (2007). Summary: We investigate a three-species food chain model with diffusion and ratio-dependent predation functional response. We mainly focus on the coexistence of the three species. For this coupled reaction-diffusion system, we study the persistent property of the solution, the stability of the constant positive steady state solution, and the existence and nonexistence of nonconstant positive steady state solutions. Both the general stationary pattern and Turing pattern are observed as a result of diffusion. Our results also exhibit some interesting effects of diffusion and functional responses on pattern formation. Cited in 1 ReviewCited in 57 Documents MSC: 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92C15 Developmental biology, pattern formation 92D40 Ecology Keywords:food chain model; diffusion; ratio-dependent functional response; stationary pattern; Turing pattern; steady state solution PDF BibTeX XML Cite \textit{R. Peng} et al., SIAM J. Appl. Math. 67, No. 5, 1479--1503 (2007; Zbl 1210.35268) Full Text: DOI OpenURL