Analysis of ratio-dependent food chain model

In this paper, a food chain model with ratio-dependent functional response is studied under homogeneous Neumann boundary conditions. The large time behavior of all non-negative equilibria in the time-dependent system is investigated, i.e., conditions for the stability at equilibria are found. Moreover, non-constant positive steady-states are studied in terms of diffusion effects, namely, Turing patterns arising from diffusiondriven instability (Turing instability) are demonstrated. The employed methods are comparison principle for parabolic problems and Leray–Schauder Theorem. © 2007 Elsevier Inc. All rights reserved.