一类具有双时滞的四种群的随机捕食-食饵模型的解及渐近行为

本文讨论了一类特殊的带有双时滞的四种群的随机捕食-食饵模型.我们首先证明了该随机捕食-食饵模型对正的初始条件存在着唯一的全局正解.然后,通过构造适当的Lyapunov函数并结合伊藤公式的应用,从解在平衡点附近的渐近行为这一方面对随机模型进行了讨论.最后,利用常微分方程数值模拟来验证本文定理中的主要结论.

Solutions and Asymptotic Behavior of a four Species Random Predator-Prey Model with Double Time Delays

In this paper,we discuss a special four-species stochastic predator-prey model with double delays.We first prove that the stochastic predator-prey model has a unique global positive solution to the positive initial conditions.Then,by constructing the appropriate Lyapunov function and combining the application of Ito’s formula,the stochastic model is discussed from the gradual progress of the solution near the equilibrium point.Finally,numerical simulation of ordinary differential equation is used to verify the main conclusions in the theorem of this paper.