Cushing J M, Saleem M
J Math Biol. 1982;14(2):231-50. doi: 10.1007/BF01832847.
A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects it fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and de-stabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation period m of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for small m or are destabilized as m decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.
考虑一个一般的捕食者 - 猎物模型，其中假设捕食者种群具有年龄结构，该年龄结构会显著影响其繁殖力。模型方程是从适用于年龄结构种群的一般麦肯德里克方程推导出来的。研究了平衡点的存在性、稳定性和失稳情况，它们取决于猎物的自然承载能力和捕食者的成熟期(m)。本文的主要结果是，对于一大类成熟函数，正平衡点要么在(m)较小时不稳定，要么随着(m)减小到零而失稳。这与通常的经验法则相反，即生长率响应的延迟增加（而非减少）会导致不稳定性。
