Special Feature: The 1st Takagi Lecture

Japanese Journal of Mathematics

, Volume 2, Issue 1, pp 197-227

First online:

On the mathematics of emergence

  • Felipe CuckerAffiliated withDepartment of Mathematics, City University of Hong Kong Email author 
  • , Steve SmaleAffiliated withToyota Technological Institute at Chicago

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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.

Keywords and phrases:

emergence flocking consensus reaching

Mathematics Subject Classification (2000):

92D50 92D25 91D30