基于尺度结构的周期三种群系统的最优收获

Optimal harvesting for three species system with size-structures in periodic environments

在周期环境下研究依赖尺度结构的三维食物链模型的最优收获问题。首先,运用Banach不动点定理推导出系统非负有界解的存在唯一性,其次运用切锥-法锥概念得出最优控制问题的解为最优的必要条件,最后,通过Ekeland变分原理,证明最优控制的存在唯一性。

The paper investigates the optimal harvesting for three-dimensional food chain model with size-structures in periodic environments.Firstly,by applying the theorem of Banach fixed point,we establish the existence and uniqueness of nonnegative bounded solutions.Secondly,we obtain the necessary conditions by using the tangent-normal cones.Finally,on the basis of Ekeland’s variational principle,we conclude that a unique optimal policy exists.