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Global behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy. (English) Zbl 1157.34349

Summary: Global behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy is investigated. Four new sufficient conditions that guarantee the exponential stability of the impulsive evolution operator introduced by us are given. By virtue of exponential stability of the impulsive evolution operator, we present the existence, uniqueness and global asymptotical stability of periodic solutions. Further, the existence result of periodic optimal controls for a Bolza problem is given. At last, an academic example is given for demonstration.

MSC:

34K13 Periodic solutions to functional-differential equations
92D25 Population dynamics (general)
93C15 Control/observation systems governed by ordinary differential equations
34K35 Control problems for functional-differential equations
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