Multiscale analysis of collective motion and decision-making in swarms: An advection-diffusion equation with memory approach

M. Raghib, S. A. Levin, I. G. Kevrekidis

Research output: Contribution to journalArticle

11 Scopus citations

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 languageEnglish (US)
Pages (from-to)893-913
Number of pages21
JournalJournal of Theoretical Biology
Volume264
Issue number3
DOIs
StatePublished - Jun 1 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Keywords

  • Anomalous transport
  • Collective animal behavior
  • Continuous time random walks
  • Non-Gaussian statistics
  • Non-Markovian stochastic processes
  • Self-propelled particle models

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