一类C-M型功能反应的时滞随机捕食系统的性态

Behavior of Same Class Time-Delay Stochastic Predator-Prey Systems with C-M Functional Type Response

针对一类具有Crowley-Martin型功能反应的时滞随机捕食系统,运用It公式、Lyapunov函数方法和Chebyshev不等式,讨论了系统正解的全局存在唯一性及系统解的随机最终有界性;运用随机比较定理获得了系统中食饵和捕食者种群的灭绝及平均持续生存的充分条件.

For a class of time-delay stochastic predator-prey systems with Crowley-Martin type functional response,the global existence and uniqueness of the positive solution of the system and the stochastic final boundedness of the system solution are discussed by using It formula、Lyapunov function method and Chebyshev inequality,sufficient conditions for the extinction and average persistence of prey and predator in the system are obtained by using stochastic comparison theorem.