一类随机互惠模型的遍历性和最优收获策略  

Ergodicity and Optimal Harvesting Policy for a Stochastic Mutualism Model

作　　者：罗俊威 LUO Jun-wei(School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China)

机构地区：[1]南京财经大学应用数学学院,南京210023

出　　处：《重庆工商大学学报（自然科学版）》2021年第4期68-72,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金项目资助(11601225).

摘　　要：讨论一个非线性生物互惠模型在随机扰动环境下的性质特征,以及最优收获策略问题。为了解模型系统的动力学特征,首先利用随机方程的比较原理证明系统解的存在唯一性,并给出两物种平均持续存在的条件;然后利用集合和遍历的方法得到最优收获策略的表达形式,且利用数值模拟直观表现物种在捕获条件下的生长情况,并与所得的理论结果吻合;这帮助人类在充分获取自然资源并获得最大收益的同时,也能使物种生物量维持在一个合理的水平,避免物种灭绝,保证生物多样性。The properties of a nonlinear mutualism model under stochastic perturbations are discussed along with the problem of the optimal harvesting strategy.In order to study the dynamic behaviors,the existence and uniqueness of positive solution to the model are proven by the comparison principle of stochastic equations,and the criteria for persistence in mean and extinction of two species are given.Finally,by using the aggregation and ergodic method,the explicit form of optimal harvesting policy is obtained,together with the numerical stimulation showing the growth situations of two species under exploitation,which not only help human beings take fully advantage of nature and gain maximum benefit,but maintain populations at a reasonable level,keep species from extinction,and guarantee the biodiversity.

关 键 词：最优收获策略 随机互惠模型 持续与灭绝 遍历性 Itô公式 

分 类 号：O175.13[理学—数学] O29[理学—基础数学]