Identifying the Nonlinear Dynamics of Logistic Mapping Using the Modified 0–1 Test for Chaos

Abstract

Chaos identification can not only promote the development and perfection of chaos theory, but also help to find the factors that produce chaos in the considered system, and control or anti-control it. The 0–1 test for chaos is an effective method to detect chaos. In order to simulate the noise contaminated through its production, Gaussian, Exponential, and Uniform noises are added to Logistic mapping to form a new hybrid time series, respectively. The effects of noise types and levels on the modified 0–1 test for chaos are studied. By studying the effect of different types of noises on chaos index [Formula: see text], [Formula: see text], and the change of [Formula: see text] with amplitude [Formula: see text], it can be seen that Uniform noise has the greatest effect on chaos identification. In addition, it is found that the effect of the noise types on chaos identification depends on the peak of the noisy time series, and the effect of the noise on chaos detection increases with the increase of the noisy time series peak. It is worth noting that the selection of amplitude [Formula: see text] can improve the noise resistance of chaos identification. The noise resistance of the modified 0–1 test for chaos can be improved by adjusting the amplitude [Formula: see text] of the parameters. With the continuous increase of noise contamination level, the effect on the modified 0–1 test for chaos detection results is gradually enhanced, so reducing the noise contamination level is the key to improving the accuracy of the modified 0–1 test for chaos. In addition, adjusting the amplitude [Formula: see text] can also play a certain noise immunity effect, and when [Formula: see text], the noise immunity is stronger on logistic mapping. Sample size [Formula: see text] up to [Formula: see text] is sufficient, but amplitude [Formula: see text] has little effect on chaos identification.