Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Persistence and global asymptotic stability of single species dispersal models with stage structure

Authors: H. I. Freedman and J. H. Wu
Journal: Quart. Appl. Math. 49 (1991), 351-371
MSC: Primary 92D25; Secondary 34K20
DOI: https://doi.org/10.1090/qam/1106397
MathSciNet review: MR1106397
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Abstract: A system of retarded functional differential equations is proposed as a model of single-species population growth with dispersal in a multi-patch environment where individual members of the population have a life history that takes them through two stages, immature and mature. The persistence of the system as well as the existence and global asymptotic stability of a positive equilibrium is proved by using the monotone dynamical systems theory due to Hirsch and Smith, and a convergence theorem established in this paper for nonautonomous retarded equations by using limiting equations theory.

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DOI: https://doi.org/10.1090/qam/1106397
Article copyright: © Copyright 1991 American Mathematical Society

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