Permanence of general stage-structured consumer-resource models

Authors:
Shengqiang Liu;Zhuojun Liu
Affiliations:
Research Center of sciences, Harbin Institute of Technology, Harbin 150001, P.R. China and College of Applied Sciences, Beijing University of Technology, Beijing 100022, P.R. China;Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P.R. China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Permanence of general stage-structured consumer-resource models

Journal of Computational and Applied Mathematics

Permanence of general stage-structured consumer-resource models

Journal of Computational and Applied Mathematics

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Abstract

Much of the existing stage-structured consumer-resource models ignore the permanence. In this paper, we consider the permanence for a series of staged-structured consumer-resource models with the function response of so-called ''prey-dependence''(resource-dependence) type. We show that the systems are permanent, if and only if the adult consumer's recruitment rate at the peak of resource abundance is more than its death rate. Our results indicate that the large consumer's maturation time delay will directly lead to its extinction. Furthermore, our arguments for the main results give a light for permanence in the general stage-structured consumer-resource systems.