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: 探讨了污染环境下具有个体尺度结构与时滞效应随机种群模型的最优控制问题.利用特征线法证明了系统解存在的唯一性,给出了最优控制的存在性;应用哈密顿函数得到最优控制的一阶必要条件,并绘制了相应的二维图.结果表明,孕育时滞延长会推迟种群的最佳收获期,环境随机因素增大则加剧种群振荡幅度,减小资源利用空间.

     

    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.

     

/

返回文章
返回