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

416 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

Access Output

10.1007/s11537-007-0647-x

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{627f6b5f04534d3a99e463ec826be97f,

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.",

keywords = "Consensus reaching, Emergence, Flocking",

author = "Felipe Cucker and Steve Smale",

year = "2007",

month = mar,

doi = "10.1007/s11537-007-0647-x",

language = "English",

volume = "2",

pages = "197--227",

journal = "Japanese Journal of Mathematics",

issn = "0289-2316",

publisher = "Springer Japan",

number = "1",

}

TY - JOUR

T1 - On the mathematics of emergence

AU - Cucker, Felipe

AU - Smale, Steve

PY - 2007/3

Y1 - 2007/3

N2 - 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.

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

KW - Emergence

KW - Flocking

UR - http://www.scopus.com/inward/record.url?scp=34047112216&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-34047112216&origin=recordpage

U2 - 10.1007/s11537-007-0647-x

DO - 10.1007/s11537-007-0647-x

M3 - RGC 21 - Publication in refereed journal

SN - 0289-2316

VL - 2

SP - 197

EP - 227

JO - Japanese Journal of Mathematics

JF - Japanese Journal of Mathematics

IS - 1

ER -

On the mathematics of emergence

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this