Direct observation of crises of the chaotic attractor in a nonlinear oscillator

Abstract

For a driven nonlinear oscillator we report direct evidence for three cases of an interior crisis of the attractor, as conjectured by Grebogi, Ott, and Yorke. These crises are sudden and discontinuous changes in the attractor, observed directly from bifurcation diagrams and attractor diagrams (Poincaré sections) in real time. The crises arise from intersection of an unstable orbit with the chaotic attractor.