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Viability theory : an applied mathematics tool for achieving dynamic systems' sustainability

Identyfikatory
Warianty tytułu
PL
Teoria wiabilności : narzędzie matematyki stosowanej do ujawniania stanów zrównoważonego rozwoju
Języki publikacji
EN
Abstrakty
EN
Sustainability is an issue of paramount importance, as scientists and politicians seek to understand what it means, practically and conceptually, to be sustainable. This paper’s aim is to introduce viability theory, a relatively young branch of mathematics which provides a conceptual framework that is very well suited to such problems. Viability theory can be used to answer important questions about the sustainability of systems, including those studied in macroeconomics, and can be used to determine sustainable policies for their management. The principal analytical tool of viability theory is the viability kernel which describes the set of all state-space points in a constrained system starting from which it is possible to remain within the system’s constraints indefinitely. Although, in some circumstances, kernel determination can be performed analytically, most practical results in viability theory rely on graphical approximations of viability kernels, which for nonlinear and high-dimensional problems can only be approached numerically. This paper provides an outline of the core concepts of viability theory and an overview of the numerical approaches available for computing approximate viability kernels. VIKAASA, a specialised software application developed by the authors and designed to compute such approximate viability kernels is presented along-side examples of viability theory in action in the spheres of bio-economics and macroeconomics.
PL
Zrównoważony rozwój jest terminem często używanym lecz naukowcy i politycy nie są zgodni ani co do jego znaczenia, ani jak praktycznie i teoretycznie zapewnić taki rozwój. Niniejsza praca ma na celu wprowadzenie czytelnika do teorii wiabilności30, stosunkowo młodej gałęzi matematyki ciągłej, której narzędzia nadają się do opisu problemów zrównoważonego rozwoju. W szczególności, teoria wiabilności może być wykorzystana do określania strategii zrównoważonego rozwoju systemów ekonomicznych, w tym makroekonomicznych. Głównym narzędziem analitycznym teorii wiabilności jest jądro wiabilności, którym jest zbiór wszystkich punktów przestrzeni stanu, z jakich mogą się dokonać ewolucje systemu, które nigdy nie przekroczą zadanych z góry ograniczeń. Chociaż w pewnych okolicznościach opis jądra może być otrzymany analitycznie, większość praktycznych rezultatów w teorii wiabilności uzyskuje się przez analizę graficznych przybliżeń jąder wiabilności, które w przypadku nieliniowych i wysokowymiarowych problemów mogą być uzyskane jedynie drogą obliczeniową. Niniejsza praca przedstawia podstawowe pojęcia teorii wiabilności oraz przegląd dostępnych metod numerycznych do obliczania przybliżeń jąder. VIKAASA, specjalistyczne oprogramowanie opracowane przez autorów, umożliwia otrzymywanie takich przybliżeń. W pracy, użycie VIKAASY jest zilustrowane przykładami z zakresu bio- i makroekonomii.
Rocznik
Strony
97--126
Opis fizyczny
Bibliogr. 47 poz., rys.
Twórcy
  • Victoria University of Wellington PO Box 600, Wellington 6140, New Zealand
autor
  • Victoria University of Wellington PO Box 600, Wellington 6140, New Zealand
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0438de9c-52d6-42b2-83e5-c4d61d0e8472
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