Asymptotics for a class of iterated random cubic operators

A. J. Homburg, U. U. Jamilov, M. Scheutzow

Research output: Contribution to JournalArticleAcademicpeer-review


We consider a class of cubic stochastic operators that are motivated by models for evolution of frequencies of genetic types in populations. We take populations with three mutually exclusive genetic types. The long term dynamics of single maps, starting with a generic initial condition, is asymptotic to equilibria where either only one genetic type survives, or where all three genetic types occur. We consider a family of independent and identically distributed maps from this class and study its long term dynamics, in particular its random point attractors. The long term dynamics of the random composition of maps is asymptotic, almost surely, to equilibria. In contrast to the deterministic system, for generic initial conditions these can be equilibria with one or two or three types present (depending only on the distribution).

Original languageEnglish
Pages (from-to)3646-3660
Number of pages15
Issue number10
Early online date30 Aug 2019
Publication statusPublished - Oct 2019


  • intermingled basins
  • random point attractors
  • random Volterra operators


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