文章研究了基于尺度结构的捕食-食饵种群系统的最优收获率控制问题,通过控制种群的收获率使得种群分布达到理想状态并使收获成本最小.首先借助不动点定理证明了系统解的存在唯一性,其次导出共轭系统并利用切锥-法锥理论给出了收获控制为最优的必要性条件.

The optimal harvest rate control problem for a predator-prey system with size-structure is studied in this paper. First of all, the existence and uniqueness of the solution is proved by using the fixed point theorem. Then, the adjoint system is derived and the necessary conditions for optimal harvesting control are obtained by means of tangent and normal cones.