Chaos and Unpredictability in Evolutionary Dynamics in Discrete Time Articles uri icon

publication date

  • July 2011

start page

  • 1

end page

  • 4

issue

  • 3 (038101)

volume

  • 107

International Standard Serial Number (ISSN)

  • 0031-9007

Electronic International Standard Serial Number (EISSN)

  • 1079-7114

abstract

  • A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from those of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace the usual fixed-point population solutions. We observe the familiar period-doubling and chaotic-band-splitting attractor cascades of unimodal maps but in some cases more elaborate variations appear due to bimodality. Also unphysical stationary solutions can have unusual physical implications, such as the uncertainty of the final population caused by sensitivity to initial conditions and fractality of attractor preimage manifolds.