Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems

This manual introduces and provides usage details for an application we have developed called VIKAASA, as well as the library of functions underlying it. VIKAASA runs in GNU Octave or MATLAB®, using the numerical computing and graphing capabilities of those packages to approximate, visualise and test viability kernels for viability problems involving a differential inclusion of two or more dynamic variables, a rectangular constraint set and a single scalar control

InfsocSol3: An updated MATLAB® package for approximating the solution to a continuous-time infinite horizon stochastic optimal control problem

This paper describes a suite of MATLAB® routines devised to provide an approximately optimal solution to an infinite-horizon stochastic optimal control problem. The suite is an updated version of that described in [1] and [2]. Its routines implement a policy improvement algorithm to optimise a Markov decision chain approximating the original control problem, as described in [3]

Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems

This manual introduces and provides usage details for an application we have developed called VIKAASA, as well as the library of functions underlying it. VIKAASA runs in GNU Octave or MATLAB®, using the numerical computing and graphing capabilities of those packages to approximate, visualise and test viability kernels for viability problems involving a differential inclusion of two or more dynamic variables, a rectangular constraint set and a single scalar control. This document details version 2.0 of the software

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

 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

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

 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

Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems

This manual introduces and provides usage details for an application we have developed called VIKAASA, as well as the library of functions underlying it. VIKAASA runs in GNU Octave or MATLAB®, using the numerical computing and graphing capabilities of those packages to approximate, visualise and test viability kernels for viability problems involving a differential inclusion of two or more dynamic variables, a rectangular constraint set and a single scalar control

Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems

This manual introduces and provides usage details for an application we have developed called VIKAASA, as well as the library of functions underlying it. VIKAASA runs in GNU Octave or MATLAB®, using the numerical computing and graphing capabilities of those packages to approximate, visualise and test viability kernels for viability problems involving a differential inclusion of two or more dynamic variables, a rectangular constraint set and a single scalar control.Computational economics, Viability theory, VIKAASA,