带有Ornstein-Uhlenbeck过程的随机logistic种群模型  

A Stochastic Logistic Population Model Incorporating Ornstein-Uhlenbeck Process

作　　者：师婉影 魏春金[1] 张树文[1] SHI Wanying;WEI Chunjin;ZHANG Shuwen(School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2023年第1期83-90,共8页Journal of Jimei University：Natural Science

基　　金：国家自然科学基金项目(11971405);福建省自然科学基金项目(J01418);集美大学国家自然科学基金培育项目(ZP2020064).

摘　　要：研究带有均值回复Ornstein-Uhlenbeck过程的随机logistic种群模型的动力学行为。证明收获努力E可以控制随机微分方程模型的随机灭绝和持续:若E≥E^(*)并且满足一些其他条件,则种群灭绝;若E<E,则种群持续。同时得到小的回复速率θ或大的波动强度ξ会抑制种群增长,大的回复速率θ或小的波动强度ξ有利于种群增长。In this paper,the dynamics of a stochastic logistic population model incorporating Ornstein-Uhlenbeck process were investigated,and it was proved that the harvesting effort E could be used to govern the stochastic extinction and persistence for stochastic model:if E≥E^(*) under extra conditions,N(t)will die out,while if E<E,N(t)will persist.Furthermore,it was proved that smaller speed of reversionθor bigger intensity of volatilityξcould suppress the population growth,while bigger speed of reversionθor smaller intensity of volatilityξcould benefit the population growth.

关 键 词：ORNSTEIN-UHLENBECK过程 灭绝性 持久性 种群模型 

分 类 号：O211.63[理学—概率论与数理统计]