METHODS FOR DISCRIMINATION OF STRANGE NONCHAOTIC ATTRACTORS IN QUASI-PERIODICALLY DRIVEN DUFFING OSCILLATOR

Strange nonchaotic dynamics is a new topic in the field of nonlinear dynamics. In this work, we take the quasi-periodically driven Duffing oscillator as an example to analyze the generation of strange nonchaotic attractors (SNAs). The existence of SNAs is investigated using three-dimensional Poincaré sections and quantitative methods such as Fourier transform, Lyapunov exponents, Lyapunov dimension, correlation dimension, and box dimension. The results indicate that Fourier transform is incapable of determining chaotic and strange nonchaotic behaviors. However, Lyapunov exponents and Lyapunov dimension can serve as indicators for detecting chaotic and nonchaotic behavior in the system. Correlation dimension and box dimension can clearly indicate the strangeness and nonstrangeness of the system, thus prove the existence of SNAs in the quasi-periodically driven Duffing oscillator and provide guidance for detecting SNAs in similar systems.