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Optimal impulsive harvest policy for time-dependent logistic equation with periodic coefficients. (English) Zbl 1031.92028
Summary: We study a time-dependent logistic equation with periodic coefficients. First, we show that the impulsive harvest population equation has impulsive periodic solutions for constant effort harvest and for proportional harvest. Second, we investigate the optimal harvest effort that maximizes the sustainable yield per unit of time. Then we determine the corresponding optimal population levels. Our results generalize results presented by X. Zhang et al. [Nonlinear Anal., Real World Appl. 4, 639-651 (2003; Zbl 1011.92052)].

MSC:
92D40 Ecology
34A37 Ordinary differential equations with impulses
34C25 Periodic solutions to ordinary differential equations
49N30 Problems with incomplete information (optimization)
49J15 Existence theories for optimal control problems involving ordinary differential equations
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