Publication Abstract

Plankton-generated chaos in themodelled dynamics of haddock

J.W. Horwood

Theory recentlydeveloped elsewhere is introduced, to a more applied and biological audience, for theoptimal control of linear systems with a risk-sensitive exponential of a quadratic (LEQG)cost function, and for the optimal control of fully nonlinear systems through therisk-sensitive maximum principle (RSMP). The LEQG theory is extended, in thisstudy, to give solutions for locally optimal stochastic control of nonlinear systems.Examples and applications are given of the extended theory, using simple, heuristiclogistic models and more complex multicohort models of fisheries. Implementations of thenonlinear RSMP are described. The results show how the theories can be applied tobiological harvesting and control problems. They also shed some light upon the characterof the dynamics of the risk-sensitive optimal solutions, which have been little explored.

Reference:

J.W. Horwood, 1996. Plankton-generated chaos in the modelled dynamics of haddock. I.M.A.Jour. Math. Appl. Med. Biol., 13: 35-71.