The Effect of Noise on the Structure of Strange Attractors

Phys. Lett. A 85, 20 (1981)https://ireap.umd.edu/10.1016/0375-9601%2881%2990628-91981Journal ArticleComplex and Emergent Systems

A simple model for the study of the effect of noise on the structure of strange attractors is presented, and an explicit solution for the resulting time asymptotic distribution function is obtained. As the noise level is decreased, the distribution function exhibits the Cantor set structure of the strange attractor on successively finer scales. Letting the noise level approach zero, a formal expression for the distribution function on the strange attractor is obtained.