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

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

Pages: 4627 - 4646, Volume 33, Issue 10, October 2013      doi:10.3934/dcds.2013.33.4627

 
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Hal L. Smith - School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, United States (email)
Horst R. Thieme - School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States (email)

Abstract: 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.

Keywords:  Discrete time, structured population model, persistence, persistence attractor, stability.
Mathematics Subject Classification:  Primary: 37N25, 92D25; Secondary: 37B25.

Received: September 2012;      Revised: January 2013;      Available Online: April 2013.

 References