污染环境下具有Markov切换的随机食饵-捕食渔业模型及其最优收获  

Optimal Harvesting for a Stochastic Prey-Predator Fishery Model with Markovian Switching in a Polluted Environment

作　　者：钟琪琪 韦煜明 ZHONG Qiqi;WEI Yuming(College of Intelligent Medicine and Biotechnology,Guilin Medical University,Guilin 541199,China;School of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,China)

机构地区：[1]桂林医学院智能医学与生物技术学院,广西桂林541199 [2]广西师范大学数学与统计学院,广西桂林541006

出　　处：《应用数学》2024年第2期303-320,共18页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11961074)。

摘　　要：本文研究在污染环境中具有白噪声和Markov切换的随机食饵-捕食者渔业模型的最优收获策略.首先证明全局正解的存在唯一性,讨论种群灭绝和持久的阈值.通过构造适当的Lyapunov函数得到遍历平稳分布存在的充分条件.应用遍历方法研究模型的最优收获策略.最后,提供一些数值模拟来证明理论分析.分析表明, Markov切换可以抑制种群的灭绝,而白噪声强度和污染物浓度对最优收获策略有明显的负面影响.This article investigates the optimal harvesting strategy of a stochastic prey-predator fishery model with white noise and Markovian switching in a polluted environment.The existence and uniqueness of the positive global solution are first shown.It discusses thresholds for population extinction and persistence.The sufficient condition for the existence of an ergodic stationary distribution is derived by constructing an appropriate Lyapunov function.The ergodic method is applied to study the optimal harvesting strategy of the model.Finally,some numerical simulations are provided to demonstrate the theoretical analysis.The analysis shows that Markovian switching could suppress the extinction of species,while white noise intensity and pollutant concentration have a significant negative effect on optimal harvesting.

关 键 词：食饵-捕食者模型 最优收获 环境污染 Markov切换 

分 类 号：O175[理学—数学]