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Center for Nonlinear Studies |
We propose a (time) multiscale method for the coarse-grained analysis of collective motion and decision-making in self-propelled particle models of swarms comprising a mixture of naive and informed individuals, used to address questions related to collective motion and collective decision-making in animal groups. The method is based on projecting the particle configuration onto a single `meta-particle' that consists of the elongation of the flock together with the mean group velocity and position. We find that the collective states of the configuration can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle, which we assume follows a decoupled continuous time random walk (CTRW). The mesoscopic properties of this system can be accurately predicted by an advection-diffusion equation with memory (ADEM) whose parameters are obtained from a mean group velocity time series obtained from a single simulation run of the individual-based model. Joint work with Simon Levin (Ecology and Evolutionary Biology - Princeton) and Yannis Kevrekidis (Chemical Engineering - Princeton)
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