一类食饵–捕食者随机离散时滞模型的稳定性
Stability of a Class of Prey-Predator Stochastic Discrete Model with Delay
摘要: 基于随机白噪声扰动与系统状态和平衡状态的偏差成正比，本文提出并研究了一类随机的食饵–捕食者离散时滞模型。通过Lyapunov泛函及随机微分方程动力系统的相关理论，得到了该系统正平衡状态的局部渐近均方稳定性及两个边界平衡状态的几乎确定的渐近稳定性的充分条件。理论的结果得到了数值模拟的支持。
Abstract: Based on the fact that the stochastic white noise perturbations are proportional to the deviation of the system state from the equilibrium state, a stochastic prey-predator discrete delay model is proposed and studied in this paper. By the approach of Lyapunov functional and related theories of dynamical systems of stochastic differential equations, the sufficient conditions for local asymptotic mean square stability of positive equilibrium state and almost surely asymptotic stability of two boundary equilibrium states are established. The obtained main results are supported by numeri-cal simulations.
文章引用：储家蕊, 李艳, 廖新元. 一类食饵–捕食者随机离散时滞模型的稳定性[J]. 应用数学进展, 2022, 11(12): 8936-8946. https://doi.org/10.12677/AAM.2022.1112943

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