北京师范大学学报（自然科学版）2026，Vol.62Issue(4)：440-446,7.DOI:10.12202/j.0476-0301.2026089
污染环境中具有时滞随机种群系统的最优控制
Optimal control of time-delay stochastic population systems in polluted environments
摘要
Abstract
To investigate the optimal control problem for a stochastic population model incorporating individual size structure and time-delay under pollution stress,the method of characteristics is adopted to prove the existence and uniqueness of the system solution and to establish the existence of the optimal control.The first-order necessary conditions for optimal control are derived via the Hamiltonian function,accompanied by corresponding two-dimensional diagrams.The results indicate that a longer gestation delay postpones the optimal harvesting period of the population,whereas increased environmental stochasticity amplifies population oscillations and constrains resource utilization.关键词
最优控制/随机种群系统/污染环境/尺度结构/时滞Key words
optimal control/stochastic population system/polluted environments/size structure/time-delay分类
数理科学引用本文复制引用
张昕,王战平..污染环境中具有时滞随机种群系统的最优控制[J].北京师范大学学报（自然科学版）,2026,62(4):440-446,7.基金项目
国家自然科学基金资助项目(72464026) （72464026）
宁夏自然科学基金资助项目(2026AAC030097) （2026AAC030097）
