A nonlinear oscillator with strange attractors featured Sinai-Ruelle-Bowen measure

Abstract

This paper studies a class of Duffing oscillator with a forcing parameter ϵ. We obtain Hénon-like attractors, rank one attractors, and periodic sinks as ϵ changes. Hénon-like attractors and rank one attractors are chaotic in the sense of SRB measures, while periodic sinks represent stable dynamics with a basin of positive Lebesgue measure. As ϵ→0, three attractors construct a dynamical pattern repeating with certain period. Through numerical simulations, we observe three attractors perfectly as well as the dynamical pattern.