Chaos and unpredictability in evolutionary dynamics in discrete time

Details Chaos and unpredictability in evolutionary dynamics in discrete time Chaos and unpredictability in evolutionary dynamics in discrete time

2011-03-08

arxiv.org/abs/1103.1484v2

Physical Review Letters 107, 038101 (2011)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.107.038101

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that 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 have unusual physical implications, such as uncertainty of final population caused by sensitivity to initial conditions and fractality of attractor preimage manifolds.

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