Stage-structured models of intra- and inter-specific competition within age classes

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Fang, Jian¹  Gourley, Stephen A.²  Lou, Yijun³ 

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

[2] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

[3] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China

关键词: Competition;    Stage structure;    Delay;    Monotone system;    Exponential ordering;   

DOI  :  10.1016/j.jde.2015.09.048

来源: Elsevier

【 摘 要 】

In some species, larvae and adults experience competition in completely different ways. Simple stage structured models without larval competition usually yield a single delay equation for the adults. Using an age structured system incorporating competition among both larvae and adults, we derive a system of distributed delay equations for the numbers of larvae and adults. The system is neither cooperative nor reducible to a single equation for either variable. Positivity, boundedness and uniform strong persistence are established. Linear stability analysis of equilibria is difficult due to the strong coupling, but results are proved for small delays using monotone systems theory and exponential ordering. For small delay we prove a theorem on generic convergence to equilibria, which does not directly follow from standard theory but can be proved indirectly using comparison arguments. Finally, we consider an extension to two-strain competition and prove theorems on the linear stability of the boundary equilibria. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free