Japanese Journal of Mathematics

, Volume 2, Issue 1, pp 197–227 | Cite as

On the mathematics of emergence

Special Feature: The 1st Takagi Lecture


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 


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Copyright information

© The Mathematical Society of Japan and Springer 2007

Authors and Affiliations

  1. 1.Department of MathematicsCity University of Hong KongKowloonHong Kong
  2. 2.Toyota Technological Institute at ChicagoChicagoUSA

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