Estimating effective boundaries of population growth in a variable environment

Boundary value problems

Sonja Radosavljevic¹  Vladimir Kozlov¹  Bengt Ove Turesson¹  Uno Wennergren² 

[1] Department of Mathematics, Linkoping University, Linkoping, Sweden;Department of Physics, Chemistry, and Biology, Linkoping University, Linkoping, Sweden

关键词: age-structure;    time-dependency;    environmental variability;    population growth;    upper and lower bounds;    periodic oscillations;    35B40;    35C15;    92D25;   

DOI  :  10.1186/s13661-016-0681-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study the impact of age-structure and temporal environmental variability on the persistence of populations. We use a linear age-structured model with time-dependent vital rates. It is the same as the one presented by Chipot in (Arch. Ration. Mech. Anal. 82(1):13-25, 1983), but the assumptions on the vital rates are slightly different. Our main interest is in describing the large-time behavior of a population provided that we know its initial distribution and transient vital rates. Using upper and lower solutions for the characteristic equation, we define time-dependent upper and lower boundaries for a solution in a constant environment. Moreover, we estimate solutions for the general time-dependent case and also for a special case when the environment is changing periodically.

【 授权许可】

CC BY