Persistence and global stability for a class of discrete time structured population models | Zendy

Hal L. Smith | Zendy; Horst R. Thieme | Zendy

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Persistence and global stability for a class of discrete time structured population models

Author(s) -

Hal L. Smith,

Horst R. Thieme

Publication year - 2013

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2013.33.4627

Subject(s) - mathematics , banach space , persistence (discontinuity) , population , nonlinear system , perturbation (astronomy) , fixed point , class (philosophy) , population model , stability (learning theory) , rank (graph theory) , extinction (optical mineralogy) , cone (formal languages) , pure mathematics , mathematical analysis , combinatorics , computer science , physics , demography , algorithm , geotechnical engineering , artificial intelligence , machine learning , sociology , optics , quantum mechanics , engineering

We obtain sharp conditions distinguishing extinction from persistence and provide sufficient conditions for global stability of a positive fixed point for a class of discrete time dynamical systems on the positive cone of an ordered Banach space generated by a map which is, roughly speaking, a nonlinear, rank one perturbation of a linear contraction. Such maps were considered by Rebarber, Tenhumberg, and Towney (Theor. Pop. Biol. 81, 2012) as abstractions of a restricted class of density dependent integral population projection models modeling plant population dynamics. Significant improvements of their results are provided.

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