NON‐LINEAR DYNAMICS, COMPLEXITY AND RANDOMNESS: ALGORITHMIC FOUNDATIONS

NON‐LINEAR DYNAMICS, COMPLEXITY AND RANDOMNESS: ALGORITHMIC FOUNDATIONS Abstract In this paper I make an attempt to describe, discuss and extend a few aspects of the rich mathematical tapestry that can be woven with rigorous notions of non‐linear dynamics, complexity and randomness, in terms of algorithmic mathematics. It is a tapestry that I try to weave with economic analysis, economic theory and economic modelling in mind. All three notions – that is, non‐linear dynamics, complexity and randomness – have a rich conceptual, modelling or analytic tradition in core areas of economic theory, both at the micro and macro levels. It is the algorithmic foundation I try to provide for them that could be considered the novel contribution in this paper. Once the algorithmic foundations are in place, it is, for example, almost natural to consider the famed difficulties of obtaining closed form solutions for non‐linear, complex or random dynamic models in economics almost a trivial vestige of a pre‐simulation era in mathematical modelling. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Economic Surveys Wiley

NON‐LINEAR DYNAMICS, COMPLEXITY AND RANDOMNESS: ALGORITHMIC FOUNDATIONS

Journal of Economic Surveys, Volume 25 (3) – Jul 1, 2011

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Publisher
Wiley
Copyright
© 2011 Blackwell Publishing Ltd
ISSN
0950-0804
eISSN
1467-6419
DOI
10.1111/j.1467-6419.2010.00668.x
Publisher site
See Article on Publisher Site

Abstract

Abstract In this paper I make an attempt to describe, discuss and extend a few aspects of the rich mathematical tapestry that can be woven with rigorous notions of non‐linear dynamics, complexity and randomness, in terms of algorithmic mathematics. It is a tapestry that I try to weave with economic analysis, economic theory and economic modelling in mind. All three notions – that is, non‐linear dynamics, complexity and randomness – have a rich conceptual, modelling or analytic tradition in core areas of economic theory, both at the micro and macro levels. It is the algorithmic foundation I try to provide for them that could be considered the novel contribution in this paper. Once the algorithmic foundations are in place, it is, for example, almost natural to consider the famed difficulties of obtaining closed form solutions for non‐linear, complex or random dynamic models in economics almost a trivial vestige of a pre‐simulation era in mathematical modelling.

Journal

Journal of Economic SurveysWiley

Published: Jul 1, 2011

References

  • Iteration, automatic computers and economic dynamics
    Goodwin, Goodwin
  • Computation and economic dynamics: resurrecting the Icarus tradition
    Velupillai, Velupillai
  • Uncomputability and undecidability in economic theory
    Velupillai, Velupillai

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