污染环境中具有时滞随机种群系统的最优控制OA

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.