一类生物系统的持久性

Permanence on a Biological System

在生态学中 ,常常需要研究一个生态系统随时间增加时 ,它的种群是否持续。本文利用Lyapunov稳定性理论 ,讨论了一个四维的具有捕食性质的Lotka Volterra系统 (2 )的持久性问题 ,给出了系统 (2 )解的一致有界性、正平衡点全局渐近稳定和系统 (2 )持久的充分必要条件。

In bioecology,we usually study an ecosystem whose persistence is t→∞. In this paper,we discuss permanence on a four species prey-predator Lotka-Volterra system Ⅱ by the theory of Lyapunov's stability. Therefore, the solutions to the system Ⅱ that start in R 4 + are eventually uniformly bounded;positive equilibrium point M  is globally stable and system Ⅱ is permanent if positive equilibrium point M  exists.