On the mathematics of emergence

Felipe Cucker; Steve Smale

doi:10.1007/s11537-007-0647-x

On the mathematics of emergence

Felipe Cucker, Steve Smale

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

443 Citations (Scopus)

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. © The Mathematical Society of Japan and Springer 2007.

Original language	English
Pages (from-to)	197-227
Journal	Japanese Journal of Mathematics
Volume	2
Issue number	1
DOIs	https://doi.org/10.1007/s11537-007-0647-x
Publication status	Published - Mar 2007

Research Keywords

Consensus reaching
Emergence
Flocking

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title = "On the mathematics of emergence",

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. {\textcopyright} The Mathematical Society of Japan and Springer 2007.",

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AU - Smale, Steve

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AB - 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. © The Mathematical Society of Japan and Springer 2007.

KW - Consensus reaching

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KW - Flocking

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U2 - 10.1007/s11537-007-0647-x

DO - 10.1007/s11537-007-0647-x

M3 - RGC 21 - Publication in refereed journal

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JF - Japanese Journal of Mathematics

IS - 1

ER -

On the mathematics of emergence

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Research Keywords

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