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Optimal harvesting and stability for two species stage-structured system with cannibalism. (English) Zbl 1023.92034

Summary: The dynamics of a two species system, where the species \(x\) has two stages, an immature stage and a mature stage, and the growth of the species \(y\) is of Lotka-Volterra nature, are modeled by a system of two retarded functional differential equations and an ordinary differential equation. The mature species \(x\) prey on the immature species \(x\), while the mature species \(x\) and species \(y\) are competitive to each other. With mature species \(x\) of harvesting and immature species \(x\) of stocking, we obtain conditions for global asymptotic stability of three nonnegative equilibria and the threshold of the harvesting mature population. The optimal harvesting of the mature population is also considered.

MSC:

92D40 Ecology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34C60 Qualitative investigation and simulation of ordinary differential equation models
34K20 Stability theory of functional-differential equations
49N90 Applications of optimal control and differential games
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