Abstract
A complete ecosystem analysis may be possible from the point of view of optimal control theory. Such an analysis has three parts:
(1) Determination of model structure
(2) Determination of coefficients for a given model
(3) Determination of optimal management programs for the model obtained by (1) and (2).
The methods of optimal control theory are suitable for examining these three parts separately. The essential ingredients for each part is an optimization concept.
Only the second and third parts are examined in detail here. For concreteness, a specific model structure for a prey-predator system is used. It is then shown that certain coefficients of this model are determined directly, given that the predator feeds in such a way as to maximize his caloric intake. By adding man's external controls to the model, the system can then be managed in a fashion to minimize some cost criterion.
To illustrate this latter point, the methods of optimal control theory are used to determine a manage ment program for controlling water quality in a natural lake at minimum cost. Man's control is re presented by the application of an algacide on the phytoplankton-zooplankton (prey-predator) system in the lake. The introduction of temperature dependence as a driving force in a simple dynamical model appears to be adequate for the determination of the optimal control program.
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