Mutual interactions, potentials, and individual distance in a social aggregation

A. Mogilner, L. Edelstein-Keshet, L. Bent, A. Spiros

Research output: Contribution to journalArticle

208 Citations (Scopus)

Abstract

We formulate a Lagrangian (individual-based) model to investigate the spacing of individuals in a social aggregate (e.g., swarm, flock, school, or herd). Mutual interactions of swarm members have been expressed as the gradient of a potential function in previous theoretical studies. In this specific case, one can construct a Lyapunov function, whose minima correspond to stable stationary states of the system. The range of repulsion (r) and attraction (a) must satisfy r < a for cohesive groups (i.e., short range repulsion and long range attraction). We show quantitatively how repulsion must dominate attraction (Rrd+1 gt; c Aad+1 where R, A are magnitudes, c is a constant of order 1, and d is the space dimension) to avoid collapse of the group to a tight cluster. We also verify the existence of a well-spaced locally stable state, having a characteristic individual distance. When the number of individuals in a group increases, a dichotomy occurs between swarms in which individual distance is preserved versus those in which the physical size of the group is maintained at the expense of greater crowding.

Original languageEnglish (US)
Pages (from-to)353-389
Number of pages37
JournalJournal of Mathematical Biology
Volume47
Issue number4
DOIs
StatePublished - Oct 2003

Fingerprint

swarms
Lyapunov functions
Aggregation
Theoretical Models
Agglomeration
Swarm
Interaction
Range of data
Individual-based Model
group size
Flock
flocks
Dichotomy
Stationary States
Potential Function
herds
spatial distribution
Lyapunov Function
Spacing
Verify

Keywords

  • Animal groups
  • Individual distance
  • Individual-based model
  • Lyapunov function
  • Social aggregation

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

Mutual interactions, potentials, and individual distance in a social aggregation. / Mogilner, A.; Edelstein-Keshet, L.; Bent, L.; Spiros, A.

In: Journal of Mathematical Biology, Vol. 47, No. 4, 10.2003, p. 353-389.

Research output: Contribution to journalArticle

Mogilner, A. ; Edelstein-Keshet, L. ; Bent, L. ; Spiros, A. / Mutual interactions, potentials, and individual distance in a social aggregation. In: Journal of Mathematical Biology. 2003 ; Vol. 47, No. 4. pp. 353-389.
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