拓展的离散等级结构种群模型的稳定性

Stability of an extended discrete hierarchical population model

提出并分析一类非线性离散等级结构种群模型。证明了解的非负有界性,定义了基本再生数,建立了种群正平衡态的存在唯一性,并运用非负矩阵特征值理论获得了零平衡态的渐近稳定性与不稳定性条件。

A class of nonlinear population models with discrete hierarchical structure is formulated and analyzed.The non-negativeness and boundedness of the solutions are established,the basic reproduction number is defined,on which the existence of unique positive equilibrium is proved.Conditions for the asymptotic stability and instability of zero state are obtained by eigenvalue theory of non-negative matrices.