Pursuit and an evolutionary game

Ermin Wei, Eric W. Justh, P. S. Krishnaprasad

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

Pursuit is a familiar mechanical activity that humans and animals engage in-athletes chasing balls, predators seeking prey and insects manoeuvring in aerial territorial battles. In this paper, we discuss and compare strategies for pursuit, the occurrence in nature of a strategy known as motion camouflage, and some evolutionary arguments to support claims of prevalence of this strategy, as opposed to alternatives. We discuss feedback laws for a pursuer to realize motion camouflage, as well as two alternative strategies. We then set up a discrete-time evolutionary game to model competition among these strategies. This leads to a dynamics in the probability simplex in three dimensions, which captures the mean-field aspects of the evolutionary game. The analysis of this dynamics as an ascent equation solving a linear programming problem is consistent with observed behaviour in Monte Carlo experiments, and lends support to an evolutionary basis for prevalence of motion camouflage.

Original languageEnglish (US)
Pages (from-to)1539-1559
Number of pages21
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume465
Issue number2105
DOIs
StatePublished - May 8 2009

Keywords

  • Evolutionary game
  • Geometry of simplex
  • Motion camouflage
  • Natural frames
  • Pursuit
  • Replicator dynamics

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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