Abstract
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 'naïve' and 'informed' individuals. 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 can be associated with the transient and asymptotic transport properties of the random walk followed by the meta-particle, which we assume follows a continuous time random walk (CTRW). These properties can be accurately predicted at the macroscopic level 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.
Original language | English (US) |
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Pages (from-to) | 893-913 |
Number of pages | 21 |
Journal | Journal of Theoretical Biology |
Volume | 264 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2010 |
All Science Journal Classification (ASJC) codes
- Agricultural and Biological Sciences(all)
- Applied Mathematics
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Statistics and Probability
- Modeling and Simulation
Keywords
- Anomalous transport
- Collective animal behavior
- Continuous time random walks
- Non-Gaussian statistics
- Non-Markovian stochastic processes
- Self-propelled particle models