Multiscale analysis of collective motion and decision-making in swarms: An advection-diffusion equation with memory approach

Publication Year
2010

Type

Journal Article
Abstract

We propose a (time) multiscale method for the coarse-grained analysis of collective motion and decision-making in self-propelled particle models of swarms comprising a mixture of 'naive' and 'informed' individuals. The method is based on projecting the particle configuration onto a single 'meta-particle' that consists of the elongation of the flock together with the mean group velocity and position. We find that the collective states can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle, which we assume follows a continuous time random walk (CTRW). These properties can be accurately predicted at the macroscopic level by an advection-diffusion equation with memory (ADEM) whose parameters are obtained from a mean group velocity time series obtained from a single simulation run of the individual-based model. (C) 2010 Elsevier Ltd. All rights reserved,

Journal
Journal of Theoretical Biology
Volume
264
Issue
3
Pages
893-913
Date Published
06/2010
ISBN
0022-5193
Short Title
J. Theor. Biol.