摘要
研究了一类具有空间扩散和年龄结构的三种群捕食与被捕食系统的最优收获问题,运用Banach不动点原理讨论了系统解的存在唯一性,证明了最优收获控制的存在性,给出了最大值原理.结果可为多种群扩散系统最优控制问题的实际研究提供理论基础.
We investigate optimal harvesting problem for three age-dependent population with spatial diffusion in a predator-prey system, Both existence and uniqueness of a positive solution are proven via Banach fixed point theorem. Existence of the optimal harvesting rate control and maximum principles for problems are obtained. The results may provide a strict theoretical basis for practical research of multi-species system with diffusion in optimal control problem.
出处
《数学的实践与认识》
CSCD
北大核心
2008年第22期101-108,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金资助项目(10071033)
江苏省自然科学基金资助项目(BK20022003)
关键词
种群系统
空间扩散
最优收获
极值原理
population dynamics
spatial diffusion
optimal harvesting
maximum principle
