, Volume 18, Issue 3, pp 423-430

Optimal Harvesting and Stability for a Predator-prey System with Stage Structure

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Abstract

The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.

Supported by the National Natural Science Foundation of China (No. 10171106) and the Natural Science Foundation of Henan Province (No. 0211010400).