Heterogeneous animal group models and their group-level alignment dynamics: An equation-free approach

Publication Year
2007

Type

Journal Article
Abstract

We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for heterogeneous populations consisting of informed (on preferred directions) and uninformed individuals. The orientation of each individual is characterized by an angle, whose dynamics are nonlinearly coupled with those of all the other individuals, with an explicit dependence on the difference between the individual's orientation and the instantaneous average direction. Choosing convenient coarse-grained variables (suggested by uncertainty quantification methods) that account for rapidly developing correlations during initial transients, we perform efficient computations of coarse-grained steady states and their bifurcation analysis. We circumvent the derivation of coarse-grained governing equations, following an equation-free computational approach. (c) 2006 Elsevier Ltd. All rights reserved.

Journal
Journal of Theoretical Biology
Volume
246
Issue
1
Pages
100-112
Date Published
05/2007
ISBN
0022-5193
Short Title
J. Theor. Biol.