Japan. J. Math. 2, 197-227 (2007)

On the mathematics of emergence

Felipe Cucker, Steve Smale

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.