Spreading of families in cyclic predator-prey models

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Abstract

We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice eliminating their prey. Initially all individuals get a family name which will be carried on by their descendants. Monte Carlo simulations show that the systems with several species [Formula presented] are asymptotically approaching the behavior of the voter model, i.e., the survival probability of families, the mean size of families, and the mean-square distance of descendants from their ancestor exhibits the same scaling behavior. The scaling behavior of the survival probability of families has a logarithmic correction. In case of the voter model this correction depends on the number of species, while cyclic predator-prey models behave like the voter model with infinite species. It is found that changing the rates of invasions does not change this asymptotic behavior. As an application a three-species system with a fourth-species intruder is also discussed.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume70
Issue number1
DOIs
Publication statusPublished - Jan 1 2004

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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