An Optimal Harvesting of A Discrete Time System with Ricker Growth
In this study, the dynamic behavior of a sporadic model (prey-predator) is investigated with Ricker function growth in prey species. We also found the system has four fixed points. We set the conditions that required to achieve local stability of all fixed points. The rate of harvest in the case of being a fixed quantity in the community and the existence of the bionomic equilibruim in the absence of predator are discussed then the system is extended to an optimal harvesting policy. The Pontryagin’s maximum principle is used to solve the optimality problem. Numerical simulations have been applied to enhance the results of mathematical analysis of the system.
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