具有反馈控制和时滞的比率依赖随机Lotka-Volterra竞争−合作模型的动力学分析

Dynamics analysis of a ratio-dependent stochastic Lotka-Volterra competition-cooperation model with feedback control and time delays

研究了一类新的具有反馈控制和时滞的比率依赖随机三种群Lotka-Volterra竞争−合作生物模型.首先,证明了模型存在唯一的全局正解.其次,通过构造适当的Lyapunov函数,证明了模型的解是随机最终有界的.最后,运用伊藤公式和微分不等式放缩,得到了种群灭绝的充分条件.

A new class of ratio-dependent stochastic three-group Lotka-Volterra competition cooperation model with feedback control and time delays is investigated in this paper.Firstly,we prove that system has a unique global positive solution.Further,the stochastic ultimate boundedness of the solution for system is investigated by constructing appropriate Lyapunov function.Finally,sufficient conditions for populations extinction are obtained by using Itôformula and differential inequality scaling.