OPTIMAL HARVESTING-COEFFICIENT CONTROL OF STEADY-STATE PREY PREDATOR DIFFUSIVE VOLTERRA-LOTKA SYSTEMS

This article considers the optimal control of the harvesting of a prey -predator system in an environment. The species are assumed to be in s teady state under diffusion and Voterra-Lotka type of interaction. The y are harvested for economic profit, leading to reduction of growth ra tes; and the problem is to control the spatial distributions of harves ts so as to optimize the return. Precise conditions are found so that the optimal control can be rigorously characterized as the solution of an optimality system of nonlinear elliptic partial differential equat ions. Moreover, a constructive approximation scheme for optimal contro l is given.