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

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13 Citations (Scopus)

Abstract

We obtain sharp conditions distinguishing extinction from persis- tence and provide suffcient 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 con- sidered 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 improve- ments of their results are provided.

Original languageEnglish (US)
Pages (from-to)4627-4646
Number of pages20
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume33
Issue number10
DOIs
StatePublished - Oct 2013

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Structured Populations
Population Model
Global Stability
Persistence
Discrete-time
Rank One Perturbation
Discrete-time Dynamical Systems
Ordered Banach Space
Positive Cone
Population dynamics
Banach spaces
Population Dynamics
Extinction
Cones
Contraction
Dynamical systems
Fixed point
Projection
Dependent
Modeling

Keywords

  • Discrete time
  • Persistence
  • Persistence attractor
  • Stability
  • Structured population model

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

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