Chaos and stability in some random dynamical systems
Abstract
Nonchaotic behavior in the sense of Li and Yorke chaos in discrete
dynamical systems generated by a continuous selfmapping of a real compact inter-
val means that every trajectory can be approximated by a periodic one. Stability
of this behavior was analyzed also for dynamical systems with small random per-
turbations. In this paper we study similar properties for nonautonomous periodic
dynamical systems with random perturbations and for random dynamical systems
generated by two continuous maps and their perturbations.
dynamical systems generated by a continuous selfmapping of a real compact inter-
val means that every trajectory can be approximated by a periodic one. Stability
of this behavior was analyzed also for dynamical systems with small random per-
turbations. In this paper we study similar properties for nonautonomous periodic
dynamical systems with random perturbations and for random dynamical systems
generated by two continuous maps and their perturbations.
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PDFDOI: https://doi.org/10.2478/tatra.v51i1.152