Coarse-grained analysis of stochasticity-induced switching between collective motion states
Authored by Ioannis G Kevrekidis, Allison Kolpas, Jeff Moehlis
Date Published: 2007
DOI: 10.1073/pnas.0608270104
Sponsors:
United States National Science Foundation (NSF)
Platforms:
No platforms listed
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
Model code not found
Abstract
A single animal group can display different types of collective motion
at different times. For a one-dimensional individual-based model of
self-organizing group formation, we show that repeated switching between
distinct ordered collective states can occur entirely because of
stochastic effects. We introduce a framework for the coarse-grained, computer-assisted analysis of such stochasticity-induced switching in
animal groups. This involves the characterization of the behavior of the
system with a single dynamically meaningful ``coarse observable{''}
whose dynamics are described by an effective Fokker-Planck equation. A
``lifting{''} procedure is presented, which enables efficient estimation
of the necessary macroscopic quantities for this description through
short bursts of appropriately initialized computations. This leads to
the construction of an effective potential, which is used to locate
metastable collective states, and their parametric dependence, as well
as estimate mean switching times.
Tags
Simulation
Animal groups
Fish schools
Order
Computations