Continuous versus pulse harvesting for population models in constant and variable environment. (English) Zbl 1143.92327

Braverman, Elena; Mamdani, Reneeta

J. Math. Biol. 57, No. 3, 413-434 (2008).

Summary: We consider both autonomous and nonautonomous population models subject to either impulsive or continuous harvesting. It is demonstrated that the impulsive strategy can be as good as the continuous one, but cannot outperform it. We introduce a model, where certain harm to the population is incorporated in each harvesting event, and study it for the logistic and the Gompertz laws of growth. In this case, impulsive harvesting is not only the optimal strategy but is the only possible one.

MSC:

92D40	Ecology
34A37	Ordinary differential equations with impulses
49N90	Applications of optimal control and differential games

Keywords:

harvesting; impulsive equation; logistic model; periodic solutions; maximal sustainable yield; by-catch mortality

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