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Coarse-grained analysis



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Coarse grained analysis of stochasticity induced switching between collective motion states Allison Kolpas Jeff Moehlis and Ioannis G Kevrekidis PNAS published online Mar 27 2007 doi 10 1073 pnas 0608270104 This information is current as of March 2007 Supplementary Material Supplementary material can be found at www pnas org cgi content full 0608270104 DC1 This article has been cited by other articles www pnas org otherarticles E mail Alerts Receive free email alerts when new articles cite this article sign up in the box at the top right corner of the article or click here Rights Permissions To reproduce this article in part figures tables or in entirety see www pnas org misc rightperm shtml Reprints To order reprints see www pnas org misc reprints shtml Notes Coarse grained analysis of stochasticity induced switching between collective motion states Allison Kolpas Jeff Moehlis and Ioannis G Kevrekidis Departments of Mathematics and Mechanical Engineering University of California Santa Barbara CA 93106 and Department of Chemical Engineering and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 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



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