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.