具有年龄和阶段结构离散模型动力学行为分析

The Analysis of Dynamic Behaviors for Discrete-time Model with Age and Stage Structures

该文研究具有年龄和阶段结构的离散种群模型的动力学行为,将种群分为两阶段结构,并分别在两个阶段上考虑年龄分布,建立模型。通过计算模型矩阵雅克比矩阵的占优特征值,并比较其与1的大小关系,证明了当净再生数R0<1时,平凡平衡态全局稳定,而当R0>1时,种群将存在唯一一个非负平衡态,且是全局渐近稳定的。

Considering the age-structure in each stage,by evaluating the resulting of Jacobian matrix.We discuss the stability of the trivial steady state and the nonnegative steady state.It is shown that if the net reproductive number is smaller than one,then the trivial equilibrium is globally asymptotically stable.Under certain conditions,there exists a unique globally asymptotically stable nonnegative equilibrium provided the net reproductive number is lager than one.