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

Wonlyul  Ko; Inkyung  Ahn; Shengqiang  Liu

doi:10.3934/dcdsb.2015.20.1715

Article Contents

2015, Volume 20, Issue 6: 1715-1733. Doi: 10.3934/dcdsb.2015.20.1715

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

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

Received: August 31, 2013

Revised: July 31, 2014

Published: July 2015

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Abstract

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.

Keywords:

Consumer-resource model,
maturation delay,
general functional response,
permanence,
global stability,
Lyapunov function,
Beddington-DeAngelis/Crowley-Martin/ratio-dependent models.

Mathematics Subject Classification: 35K40, 35K57, 92D25.

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References

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