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In this work, the capture effort exerted on the adult population (or exploitable population) of a two-stage species with recruitment is considered as a control parameter to investigate the optimal exploitation of the resource, sustainability properties of the population and rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal control is derived and then solved numerically using an iterative method with Euler scheme. Simulation results show that the optimal control scheme allows us to get the sustainability of the ecosystem and to validate the model.

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