具有阶段结构和时滞比率依赖的捕食系统的持续生存和稳定性

摘要

本文研究了一类带有时滞和对捕食者进行分阶段的比率依赖的捕食模型,得到了该模型中的种群的持续生存的充分条件.通过构造Lyapunov泛函的方法,得到了该模型唯一正平衡点的局部稳定和全局稳定的充分条件.%A delayed ratio-dependent predator-prey model with stage-structure for predator is proposed and analyzed. Mathematical properties of the model equations with regard to boundedness of solutions and stability of the boundary equilibrium are analyzed; Sufficient conditions for permanence are derived. By constructing Lyapunov functionals, we obtain conditions which guarantee the local and global asymptotic stability of a positive equilibrium of the model.