Abstract
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 language | English |
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Pages (from-to) | 3646-3660 |
Number of pages | 15 |
Journal | Nonlinearity |
Volume | 32 |
Issue number | 10 |
Early online date | 30 Aug 2019 |
DOIs | |
Publication status | Published - Oct 2019 |
Keywords
- intermingled basins
- random point attractors
- random Volterra operators