Heterogeneous animal group models and their group-level alignment dynamics:
An equation-free approach
Sung Joon Moon, B. Nabet, Naomi E. Leonard, Simon A. Levin, I.G. Kevrekidis
Journal of Theoretical Biology, Vol. 246, pages 100-112, 2007.
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
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.
(Paper PDF, 582 KB)
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