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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Complex adaptive systems: Exploring the known, the unknown and the unknowable
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by Simon A. Levin PDF
Bull. Amer. Math. Soc. 40 (2003), 3-19 Request permission

Abstract:

The study of complex adaptive systems, from cells to societies, is a study of the interplay among processes operating at diverse scales of space, time and organizational complexity. The key to such a study is an understanding of the interrelationships between microscopic processes and macroscopic patterns, and the evolutionary forces that shape systems. In particular, for ecosystems and socioeconomic systems, much interest is focused on broad scale features such as diversity and resiliency, while evolution operates most powerfully at the level of individual agents. Understanding the evolution and development of complex adaptive systems thus involves understanding how cooperation, coalitions and networks of interaction emerge from individual behaviors and feed back to influence those behaviors. In this paper, some of the mathematical challenges are discussed.
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Additional Information
  • Simon A. Levin
  • Affiliation: Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey 08544-1003
  • Email: slevin@princeton.edu
  • Received by editor(s): December 12, 2000
  • Received by editor(s) in revised form: February 21, 2002
  • Published electronically: October 9, 2002
  • Additional Notes: It is a pleasure to acknowledge the support of the Alfred P. Sloan Foundation, grant award 97-3-5, and of the National Science Foundation, grant award DEB-0083566. Jonathan Dushoff and Helene Muller-Landau provided useful comments.
  • © Copyright 2002 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 40 (2003), 3-19
  • MSC (2000): Primary 92B05, 92D15, 92D40
  • DOI: https://doi.org/10.1090/S0273-0979-02-00965-5
  • MathSciNet review: 1943129