带有Ornstein-Uhlenbeck过程的随机logistic种群模型

A Stochastic Logistic Population Model Incorporating Ornstein-Uhlenbeck Process

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.