title: Chaos and unpredictability in evolutionary dynamics in discrete time.
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.
authors.affiliation: Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
authors.forename: Daniele
authors.initials: D
authors.lastname: Vilone
authors.forename: Alberto
authors.initials: A
authors.lastname: Robledo
authors.forename: Angel
authors.initials: A
authors.lastname: Sánchez
mesh_terms: D005075:Biological Evolution; D017711:Nonlinear Dynamics; D010507:Periodicity; D013997:Time Factors