Abstract algebraic-delay differential systems and age structured population dynamics

作者：Kosovalic N^*; Magpantay F M G; Chen Y; Wu J

来源：Journal of Differential Equations, 2013, 255(3): 593-609.

DOI：10.1016/j.jde.2013.04.025

• Partial differential equation
• State dependent delay
• Structured population dynamics
• Threshold type delay
• Bounded delay

We consider the abstract algebraic-delay differential system, %26lt;br%26gt;x%26apos; (t) = Ax(t) + F (x(t), a (t)), %26lt;br%26gt;a(t) = H (x(t), a(t)). %26lt;br%26gt;Here A is a linear operator on D (A) subset of X satisfying the Hille-osida conditions, x(t) %26lt;(D(A))over bar%26gt; 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.

• 出版日期2013-8-1