具有比率依赖随机食物链系统的定性分析

Qualitative Analysis of a Stochastic Ratio-Dependent Food-Chain System

研究了一类具有比率依赖随机食物链系统的动力学行为,运用随机微分方程比较定理和伊藤公式,证明了系统存在唯一正解,给出随机食物链系统的持久性和物种趋于灭绝的条件.最后,通过数值模拟验证所得结果的正确性.

In this paper, a stochastic ratio-dependent food-chain system is studied. By the comparison theorem of stochastic equations and formula, we show that there is a unique positive solution to the system and the positive solution is stochastically ultimately bounded. Moreover, under some conditions, we conclude that the stochastic model is persistent in mean. Besides, the condition for species to be extinct is established. In the end, we give some numerical simulations to confirm our theoretical analysis.