Random Perturbations of One-dimensional Chaotic Systems with Linear Type Invariant Density

Abstract

In this paper, deterministic chaotic systems with random perturbations are investigated. The stationary distribution of the chaotic system with additive random perturbations is theoretically obtained, where the invariant measure of the chaotic system is described by a linear function and random perturbations are given by independent random variables with the identical and uniform distribution. An example with numerical experiment shows the validity of results obtained in this investigation.