食饵具有阶段结构和非线性出生率的捕食-食饵系统全局稳定性研究

Global Asympototic Stability of a Population Model with Nonlinear Birth Rate and Stage Structure

研究一类食饵具有阶段结构和非线性出生率的捕食-食饵模型,借助微分方程比较原理,通过构造适当的Lyapunov函数,最终证得了保证系统各个平衡点局部稳定性条件就足以保证其全局稳定性。所得结果实质性改进和推广了前人的相应结果。

A predator-prey model with nonlinear birth rate and stage structure on prey species is revisited in this paper.By using the comparison theorem of differential equation and constructing some suitable Lyapunov function,we are able to show that the conditions which ensure the locally asymptotically stable of the equilibria is enough to ensure their globally asymptotically stable.The results supplement and complement some known results.