Coarse-grained analysis of stochasticity-induced switching between collective motion states

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 104; no. 14; pp. 5931 - 5935
• Main Authors: Kolpas, Allison, Moehlis, Jeff, Kevrekidis, Ioannis G
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 03-04-2007; National Acad Sciences
• Subjects: Animal behavior; Animals; Biological Sciences; Computer Simulation; Diffusion coefficient; Effectiveness; Mathematical manifolds; Mathematical maxima; Modeling; Models, Statistical; Motion; Parameter estimation; Probability distributions; Pseudopotentials; Simulations; Stochastic models; Stochastic Processes; Trajectories
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.0608270104

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.