# American Institute of Mathematical Sciences

August  2015, 20(6): 1715-1733. doi: 10.3934/dcdsb.2015.20.1715

## Asymptotical behaviors of a general diffusive consumer-resource model with maturation delay

 1 Department of Mathematics, Korea University, 2511, Sejong-Ro, Sejong, 339-700, South Korea, South Korea 2 The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Nan-Gang District, Harbin, 150080, China

Received  September 2013 Revised  August 2014 Published  June 2015

In this paper, we examine the asymptotic behaviors of a diffusive delayed consumer-resource model subject to homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of juvenile consumers to their maturity, and the predation is of a general type of functional response. We construct the threshold dynamics of the persistence and extinction of the consumer. Moreover, we establish the sufficient conditions for the global attractivity of the semitrivial and coexistence equilibria. Finally, we apply our results to the specific consumer-resource models with Beddington-DeAngelis, Crowley-Martin, and ratio-dependent type of functional responses.
Citation: Wonlyul Ko, Inkyung Ahn, Shengqiang Liu. Asymptotical behaviors of a general diffusive consumer-resource model with maturation delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1715-1733. doi: 10.3934/dcdsb.2015.20.1715
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