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

• Autorzy: Jacek B. Krawczyk , Alastair S. Pharo
• Języki publikacji: EN

Abstrakty

EN

 Sustainability is considered an issue of paramount importance; yet scientists andpoliticians still seek to understand what it means, practically and conceptually, tobe sustainable. This paper's aim is to introduce viability theory, a relativelyyoung branch of continuous mathematics which provides a conceptual frameworkthat is very well suited to sustainability problems.  In particular, viability theory can be used toanswer important questions about the sustainability of systems, including thosestudied in macroeconomics, and can be used to determine sustainable policies fortheir management.  The principal analytical tool of viability theory is theviability kernel which is the set of all state-space points such that it is possible for evolutions starting from each of those points to remain within the system's predetermined constraints indefinitely. Although, in some circumstances,  kernel determinationcan 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 coreconcepts of viability theory and an overview of the numerical approachesavailable for computing approximate viability kernels.  \vikaasa{}, aspecialised software application developed by the authors and designed tocompute such approximate viability kernels is presented along-side examples ofviability theory in action in the spheres of bio-economics and macroeconomics.

Słowa kluczowe

EN

viability theory, differential inclusions, sustainability

• Wydawca: Polish Mathematical Society
• Czasopismo: Mathematica Applicanda
• Rocznik: 2013
• Tom: 41
• Numer: 1

Daty

wydano

2013

online

2013-07-31

Twórcy

autor

Jacek B. Krawczyk

autor

Alastair S. Pharo

Identyfikatory

DOI

10.14708/ma.v41i1.409