, Volume 2, Issue 1, pp 197-227
Date: 28 Mar 2007

On the mathematics of emergence

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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.

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.