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An optimal harvesting policy for a system of two competitive species with periodic coefficients. (Chinese. English summary) Zbl 1192.92043
Summary: Based on a class of two competitive species models, a competitive system with periodic coefficients is considered as a non-autonomous ecological system. Firstly, we discuss the permanence of the system by using comparison theory. Then, via the Brouwer fixed point theorem and stability theory, we show the existence and uniqueness of periodic solutions of the system and global asymptotic stability of the solutions. Finally, an optimal control problem corresponding to this periodic system is considered. An optimal harvesting policy $$E_{opt}(t)$$ for the above problem is obtained.

##### MSC:
 92D40 Ecology 49N90 Applications of optimal control and differential games