PERSISTENCE AND GLOBAL STABILITY FOR A CLASS OF DISCRETE TIME STRUCTURED POPULATION MODELS

被引：18
|
作者：
Smith, Hal L. [1 ]
Thieme, Horst R. [1 ]
机构：
[1] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 10期
关键词：
Discrete time; structured population model; persistence; persistence attractor; stability; FORMULATION; EQUATIONS; DYNAMICS; SYSTEMS;
D O I：
10.3934/dcds.2013.33.4627
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：4627 / 4646
页数：20
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