一类基于个体尺度的种群模型的渐近行为

On the Asymptotic Behaviors of a Class of Population Model Based on Individual's Body Size

本文研究一类尺度结构模型的渐近行为.利用特征线法导出模型的形式解以及刻画种群出生率的Volterra积分方程.运用Laplace变换确立该方程解的动力学性态,由此洞悉种群的渐近行为由一个特征参数决定.

This paper is concerned with the long-run behaviors of a kind of size-structured population model. Formal solutions of the model and the Volterra integral equation governing the population birth rate are derived by means of the method of characteristics. The dynamics of the solutions of the equation is established by using Laplace transformation, which shows that the asymptotic behaviors of the population is decided by a characteristic parameter.