Yang, Wen-Bin; Li, Yan-Ling; Wu, Jian-Hua; Li, Hai-Xia Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses. (English) Zbl 1334.35140 Discrete Contin. Dyn. Syst., Ser. B 20, No. 7, 2269-2290 (2015). Summary: The paper is concerned with a diffusive food chain model subject to homogeneous Robin boundary conditions, which models the trophic interactions of three levels. Using the fixed point index theory, we obtain the existence and uniqueness for coexistence states. Moreover, the existence of the global attractor and the extinction for the time-dependent model are established under certain assumptions. Some numerical simulations are done to complement the analytical results. Cited in 2 Documents MSC: 35K57 Reaction-diffusion equations 35J56 Boundary value problems for first-order elliptic systems 92B05 General biology and biomathematics 35B41 Attractors Keywords:ratio-dependent; Leslie-Gower; coexistence state; global attractor; numerical simulation PDF BibTeX XML Cite \textit{W.-B. Yang} et al., Discrete Contin. Dyn. Syst., Ser. B 20, No. 7, 2269--2290 (2015; Zbl 1334.35140) Full Text: DOI References: [1] M. A. Aziz-Alaoui, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes,, Appl. Math. Lett., 16, 1069, (2003) · Zbl 1063.34044 [2] E. Beretta, Global analyses in some delayed ratio-dependent predator-prey systems,, Nonlinear Anal., 32, 381, (1998) · Zbl 0946.34061 [3] S. Cano-Casanova, Existence and structure of the set of positive solutions of a general class of sublinear elliptic non-classical mixed boundary value problems,, Nonlinear Anal. Ser. 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