Impact of damping amplitude on chaos detection reliability of the improved 0–1 test for oversampled and noisy observations
The novel chaos detection method (i.e., 0–1 test for chaos) determines the median Km(c) of asymptotic growth rates K(c) to identify whether the measured time series is chaotic or not and has been widely used in several applications. Motivated by the fact that the validity of improved 0–1 test for chaos has been confirmed for noisy and oversampled observations from various dynamics, the effect of damping term amplitude on it is further discussed for various dynamical behavior (for instance, sine-circle and Peter de Jong dynamical systems) in this paper. For the magnitude order of the limit value over 103, the diagnostic indicator Km(c) has more accurate values corresponding to a quasi-periodic route to chaos with chaotic behavior. These numerical results also clearly present that the value Km(c) is sensitive to the amplitude and the speed of decline of Km(c) changes with the amplitude can reflect the degree of chaos. The insights gained from the present study accelerate the development of advanced noise-robust methods for detecting the presence (or absence) chaos from noisy empirical measurements.
Xiao, Q., Liao, Y., Xu, W. et al. Impact of damping amplitude on chaos detection reliability of the improved 0–1 test for oversampled and noisy observations. Nonlinear Dyn (2022). https://doi.org/10.1007/s11071-022-07416-4