A link between microscopic and macroscopic models of self-organized aggregation

Tadahisa Funaki*, Hirofumi Izuhara, Masayasu Mimura, Chiyori Urabe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In some species, one of the roles of pheromones is to influence aggregation behavior. We first propose a macroscopic cross-diffusion model for the self-organized aggregation of German cockroaches that includes directed movement due to an aggregation pheromone. We then propose a microscopic particle model which is set into context with the macroscopic model. Our goal is to link the macroscopic and microscopic descriptions by using the singular and the hydrodynamic limit procedures. A hybrid model related to the macroscopic and microscopic models is also proposed as a cockroach aggregation model. This hybrid model assumes that each individual responds to pheromone concentration and moves by two-mode simple symmetric random walks. It shows that even though the movement of individuals is not directed, two-mode simple symmetric random walks and effect of the pheromone result in self-organized aggregation.

Original languageEnglish
Pages (from-to)705-740
Number of pages36
JournalNetworks and Heterogeneous Media
Issue number4
Publication statusPublished - 2012
Externally publishedYes


  • Chemotaxis
  • Cross-diffusion system
  • Hydrodynamic limit
  • Particle system
  • Reaction-diffusion system

ASJC Scopus subject areas

  • Statistics and Probability
  • General Engineering
  • Computer Science Applications
  • Applied Mathematics


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