一类基于等级结构的n维食物链系统最优收获

Optimal Harvest of an n-Dimensional Food Chain System with Hierarchical Age-structure

考虑一类具年龄等级结构的n维食物链种群系统的最优收获问题,首先利用压缩映射定理,研究系统解的适定性;其次构造极值化序列和运用相关的紧性定理证明控制问题最优解的存在性;最后通过构造共轭系统和利用法锥的概念刻画,得出最优收获问题最优解的一阶必要条件.

Optimal harvest problem of an n-dimensional food chain population system with hierarchical age-structure is considered.Firstly,the existence uniqueness of the system solution is studied by using the principle of compression mapping.Secondly,the existence of the optimal solution of the control problem is proved by using extremum sequences and the compactness theorem.Finally,by constructing appropriate conjugate systems and utilizing the concept of the cone,the first-order necessary conditions for the optimal solution of the optimal harvesting problem are obtained.