Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses

Wen-Bin Yang; Yan-Ling  Li; Jianhua Wu; Hai-Xia  Li

doi:10.3934/dcdsb.2015.20.2269

Article Contents

2015, Volume 20, Issue 7: 2269-2290. Doi: 10.3934/dcdsb.2015.20.2269

This issue Previous Article Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion Next Article

Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shannxi 710062
2.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062
3.
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710119

Received: April 30, 2014

Revised: November 30, 2014

Published: August 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57, 35J55; Secondary: 92B05.

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