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On the mathematics of emergence

Japanese Journal of Mathematics volume 2, pages 197–227 (2007)Cite this article

Abstract.

We describe a setting where convergence to consensus in a population of autonomous agents can be formally addressed and prove some general results establishing conditions under which such convergence occurs. Both continuous and discrete time are considered and a number of particular examples, notably the way in which a population of animals move together, are considered as particular instances of our setting.

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Author information

Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

    Felipe Cucker

  2. Toyota Technological Institute at Chicago, 1427 East 60th Street, Chicago, IL, 60637, USA

    Steve Smale

Authors
  1. Felipe Cucker
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  2. Steve Smale
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Corresponding author

Correspondence to Felipe Cucker.

Additional information

Communicated by: Toshiyuki Kobayashi

This article is based on the 1st Takagi Lectures that the second author delivered at Research Institute for Mathematical Sciences, Kyoto University on November 25 and 26, 2006.

Steve Smale Partially supported by an NSF grant.

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Cite this article

Cucker, F., Smale, S. On the mathematics of emergence. Jpn. J. Math. 2, 197–227 (2007). https://doi.org/10.1007/s11537-007-0647-x

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  • DOI: https://doi.org/10.1007/s11537-007-0647-x

Keywords and phrases:

  • emergence
  • flocking
  • consensus reaching

Mathematics Subject Classification (2000):

  • 92D50
  • 92D25
  • 91D30