arXiv Analytics

Sign in

arXiv:1802.06089 [nlin.AO]AbstractReferencesReviewsResources

Self-organization on Riemannian manifolds

Razvan C. Fetecau, Beril Zhang

Published 2018-02-16Version 1

We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up the model on general Riemannian manifolds and provide a framework for constructing interaction potentials which lead to equilibria that are constant on their supports. We consider such potentials for two specific cases (the two-dimensional sphere and the two-dimensional hyperbolic space) and investigate analytically and numerically the long-time behaviour and equilibrium solutions of the aggregation model on these manifolds.

Related articles: Most relevant | Search more
arXiv:1903.07456 [nlin.AO] (Published 2019-03-14)
Self-Organization and Artificial Life
arXiv:1408.1529 [nlin.AO] (Published 2014-08-07)
Self-organization in complex systems as decision making
arXiv:nlin/0509049 (Published 2005-09-27)
Ten Questions about Emergence