The modelling of economical growth under sustinable development - the application of optimal control teory
2005
Miklewska, J. (Akademia Rolnicza, Szczecin (Poland). Katedra Zastosowan Matematyki)
Growth models are used to analyse inter-temporal allocation decisions. There are close parallels between some aspects of growth models as used in economics and models in ecology. Author this paper suggests application growth models and control theory under constraints of the regional sustainable development. Paper presents optimal solutions under maximization of NPV for social discount rate. From a model, that synthesises the behaviour of such a complex nonlinear biological system, author study its properties and understand the way it works. One seeks to study the qualitative behaviour of the system, the existence of equilibria, their stability, the existence of periodic solutions. These qualitative questions are fundamental because they tell us whether or not the system is viable (the model does not predict the extinction of any species, etc). Specific problems are posed by the biological origin of the models: functions or parameters are uncertain, or unknown, what can we say on the behaviour of the model? Often, the models have a strong structure belonging to a general class of systems, for which one develops adapted techniques: for example the well-known models of Lotka-Volterra in dimension n, describing the interactions between n species
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