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Numerical computation of the optimal vector field in a fishery model.

Dieter Grass. 2010.


Many of the optimal control models analyzed in economics are formulated as discounted infinite time horizon problems, where the occurring functions are nonlinear as well in the states as in the controls. As a consequence solutions can often only be found numerically. Moreover, the long run optimal solutions are in the overwhelming cases limit sets like equilibria and/or limit cycles. Using these “trivial” solutions a BVP approach together with a continuation technique is used to calculate the parameter dependent dynamic structure of the optimal vector field. We use a one-dimensional optimal control model of fishery to exemplify the numerical techniques. But these methods, as will be shown, are applicable to a much wider class of optimal control problems with any number of state and control variables

Keywords: Optimal vector field, BVP, Continuation, Multiple optimal solutions, Threshold point

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