一类非线性年龄等级结构种群模型的稳定性

Stability of a Class of Nonlinear Hierarchical Age-Dependent Population Model

该文分析一类基于年龄的等级结构种群模型正平衡态的存在性及零解的稳定性,在年轻个体占优的前提下用偏微分-积分方程描述种群演化进程.定义了种群再生数,运用非零不动点原理确立了该系统存在正平衡态,借助特征方程和Liapunov函数导出零解的局部和全局稳定结果,并做出数值验证.

The article is concerned with the existence of positive equilibria and stability of zero state in a nonlinear hierarchical species.Based on the assumption that young individuals are more competitive than older ones,an integro-partial differential equation is taken to model the revolution process of the population.The net reproductive number is defined and used to show that there are positive steady states in the system.Furthermore,stability results for zero equilibrium are derived via the characteristic equation and a Liapunov function.Finally,some numerical experiments are presented.