Amplitude Equations for Time-Dependent Solutions of the McKendrick Equations
Amplitude Equations for Time-Dependent Solutions of the McKendrick Equations
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McKendrick 方程瞬态解的振幅方程
DOI：
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发表时间：
2001
影响因子：
1.9
通讯作者：
D. Quinn
中科院分区：
文献类型：
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作者：
C. Clemons;S. I. Hariharan;D. Quinn
McKendrick方程模拟了年龄相关种群的动力学行为。这些方程决定了在时间t时，人口中年龄为a的个体的数量，即人口密度，它是由一个守恒定律产生的，该定律服从于对生育率和死亡率的基本假设。本文给出了McKendrick方程的弱非线性分析，该分析描述了其解的分支，该解的振幅由复朗道-Stuart-type方程控制.多尺度方法的框架描述了产妇和死亡率的一般假设，并进行了详细的分析，年龄无关的死亡率和一个可分离的产妇功能，其中包括一个非零的延迟开始成熟。结果表明，时滞的存在显着影响后分岔动力学，并介绍了余维2分岔系统。
The McKendrick equations model the dynamical behavior of age-dependent populations. These equations govern, at time t, the number of individuals of age a in a population, known as the population density, and arise from a conservation law subject to constitutive assumptions for the maternity and mortality rates. In this paper, we present a weakly nonlinear analysis of the McKendrick equations which describes the bifurcation to time-dependent solutions whose amplitudes are governed by a complex Landau--Stuart-type equation. The framework of the multiple scales approach is described for general assumptions on the maternity and mortality rates, and the analysis is carried out in detail for an age-independent mortality rate and a separable maternity function which includes a nonzero delay in the onset of maturation. The resulting analysis indicates that the presence of the delay significantly affects the postbifurcational dynamics and introduces a codimension two bifurcation in the system.