Abstract
The paper deals with the problem of combined harvesting of two competing fish species, each of which obeys the law of logistic growth. It is shown that the open-access fishery may possess a bionomic equilibrium which drives one species to extinction. An analysis of the dynamic behaviour of the system reveals that its non-trivial critical point is either an asymptotically stable node or an unstable saddle point depending on the values of the biological parameters. Further, the nature of the trivial critical point (origin) is found to depend on the biotechnical productivity (btp) of each species. It is also proven that the dynamic system does not possess any limit cycles. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equilibrium case by using Pontryagin's maximal principle. Biological and economic interpretations of the results associated with the optimal equilibrium solution are explained. The significance of the results derived in the paper are then discussed.
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