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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 1715 - 1733, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1715

 
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Wonlyul Ko - Department of Mathematics, Korea University, 2511, Sejong-Ro, Sejong, 339-700, South Korea (email)
Inkyung Ahn - Department of Mathematics, Korea University, 2511, Sejong-Ro, Sejong, 339-700, South Korea (email)
Shengqiang Liu - The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Nan-Gang District, Harbin, 150080, China (email)

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.

Received: September 2013;      Revised: August 2014;      Available Online: June 2015.

 References