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Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses. (English) Zbl 1334.35140
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.

##### MSC:
 35K57 Reaction-diffusion equations 35J56 Boundary value problems for first-order elliptic systems 92B05 General biology and biomathematics 35B41 Attractors
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