Abstract algebraic-delay differential systems and age structured population dynamics

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Kosovalic, N.¹  Magpantay, F. M. G.¹  Chen, Y.²  Wu, J.¹ 

[1] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

关键词: Partial differential equation;    State dependent delay;    Structured population dynamics;    Threshold type delay;    Bounded delay;   

DOI  :  10.1016/j.jde.2013.04.025

来源: Elsevier

【 摘 要 】

We consider the abstract algebraic-delay differential system, x' (t) = Ax(t) + F (x(t), a (t)), a(t) = H (x(t), a(t)). Here A is a linear operator on D (A) subset of X satisfying the Hille-osida conditions, x(t) <(D(A))over bar> c subset of X. and a(t) is an element of R-n, where X is a real Banach space. With a global Lipschitz condition on F and an appropriate hypothesis on the function H. we show that the corresponding initial value problem gives rise to a continuous semiflow in a subset of the space of continuous functions. We establish the positivity of the x-component and give some examples arising from age structured population dynamics. The examples come from situations where the age of maturity of an individual at a given time is determined by whether or not the resource concentration density, which depends on the immature population, reaches a prescribed threshold within that time. (C) 2013 Published by Elsevier Inc.

【 授权许可】

Free