Coarse analysis of collective motion with different communication mechanisms.
We study the effects of a signalling constraint on an individual-based model of self-organizing group formation using a coarse analysis framework. This involves using an automated data-driven technique which defines a diffusion process on the graph of a sample dataset formed from a representative stationary simulation. The eigenvectors of the graph Laplacian are used to construct 'diffusion-map' coordinates which provide a geometrically meaningful low-dimensional representation of the dataset. We show that, for the parameter regime studied, the second principal eigenvector provides a sufficient representation of the dataset and use it as a coarse observable. This allows the computation of coarse bifurcation diagrams, which are used to compare the effects of the signalling constraint on the population-level behavior of the model.
Kolpas
Allison
A
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA. allie@math.ucsb.edu
Moehlis
Jeff
J
Frewen
Thomas A
TA
Kevrekidis
Ioannis G
IG
D000465:Algorithms; D000819:Animal Communication; D000818:Animals; D005399:Fishes / Q000502:physiology; D008954:Models, Biological; D009038:Motion; D017711:Nonlinear Dynamics; D025341:Principal Component Analysis; D012919:Social Behavior; D013037:Spatial Behavior / Q000502:physiology*; D013269:Stochastic Processes