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

Jacek B. Krawczyk, and Alastair S. Pharo. "Viability theory: an applied mathematics tool for achieving dynamic systems' sustainability." Mathematica Applicanda 41.1 (2013): null. <http://eudml.org/doc/293018>.

@article{JacekB2013,
abstract = { 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.  , 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.},
author = {Jacek B. Krawczyk, Alastair S. Pharo},
journal = {Mathematica Applicanda},
keywords = {viability theory, differential inclusions, sustainability},
language = {eng},
number = {1},
pages = {null},
title = {Viability theory: an applied mathematics tool for achieving dynamic systems' sustainability},
url = {http://eudml.org/doc/293018},
volume = {41},
year = {2013},
}

TY - JOUR
AU - Jacek B. Krawczyk
AU - Alastair S. Pharo
TI - Viability theory: an applied mathematics tool for achieving dynamic systems' sustainability
JO - Mathematica Applicanda
PY - 2013
VL - 41
IS - 1
SP - null
AB -  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.  , 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.
LA - eng
KW - viability theory, differential inclusions, sustainability
UR - http://eudml.org/doc/293018
ER -