一类具有反馈控制的随机贻贝-藻类模型的动力学研究

Dynamical Behavior of a Stochastic Mussel-algal Model with Feedback Control

建立了1类具有反馈控制的随机贻贝-藻类模型,该模型模拟了贻贝和藻类在随机环境下的相互作用,且同时考虑了白噪声和反馈控制的综合影响。首先证明了该模型全局唯一正解的存在性;然后应用随机微分方程的相关分析技巧,获得了贻贝的灭绝和平稳分布存在性的充分条件;最后通过数值例子验证了理论结果的可行性。结果表明,随机贻贝-藻类模型的动力学行为与白噪声及反馈控制密切相关。

In this paper, a stochastic mussel-algal model with feedback control is investigated, which simulates the interaction between mussels and algae in a stochastic environment and considers the combined effects of white noise and feedback control.Firstly, the existence of a unique global positive solution for this model is given.Then, by applying the analysis techniques of stochastic differential equations, sufficient conditions for the extinction and existence of a stationary distribution of the mussel are obtained.Finally, the theoretical results are verified by numerical examples.The results indicate that dynamic behaviors of the stochastic mussel-algae model are intimately associated with white noises and feedback control.