周期随机Gompertz模型的最优收获策略-《集美大学学报（自然科学版）》

文章信息/Info

Author(s):: WANG Fengyan; (School of Science,Jimei University,Xiamen 361021,China)

Keywords:: periodic Gompertz model; optimal harvesting; stochastic perturbations; sustainable yield; permanence

摘要:: 研究周期随机Gompertz模型的最优收获策略,得到该模型的正初始值出发的解及其均值的解析表达式。证明模型的解是依均值的平方全局吸引，并存在唯一依均值的平方全局稳定的随机解。证明周期随机Gompertz模型随机持久性，确定充要条件保证最优收获的存在性，并得到周期随机收获模型的最优收获努力量和最大期望承受依时间平均生产量。

Abstract:: This paper concerns the optimal harvesting policy for a periodic stochastic Gompertz model.It shows that the equation had a global positive solution starting from the positive initial value and obtain its explicit expression.The expectation of the solution was also obtained.It shows that the periodic stochastic Gompertz model was globally attractive in the mean square and had a unique globally attractive stochastic solution.It was established that the equation was stochastically permanent.Sufficient and necessary conditions for the existence of an optimal control were established.The optimal harvesting effort and the maximum value of the expectation of sustainable yield in the time mean were obtained as well.