Biology – Quantitative Biology – Quantitative Methods
Scientific paper
2006-06-16
Biology
Quantitative Biology
Quantitative Methods
final form; accepted for publication in Journal of Theoretical Biology
Scientific paper
We study coarse-grained (group-level) alignment dynamics of individual-based animal group models for {\it 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.
Kevrekidis Ioannis G.
Leonard Naomi Ehrich
Levin Simon A.
Moon Sung Joon
Nabet Bahram
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