Detection of Hidden Oscillations in Systems Without Equilibrium

Abstract

Chaotic systems with hidden attractors have been widely studied in recent decades. In this field, systems without equilibrium are of special interest. Since multistable systems can alternate between several hidden attractors, it is difficult to detect their hidden oscillations using known analytical techniques. In this study, we propose to apply recurrence analysis methods as a possible solution to this problem. We consider the new quantity measure, called relative specific volume, which correlates with changes of the attractor. We choose the improved Sprott A system as an example of the multiscroll attractor to verify the proposed approach. We compare the new recurrence measure with other traditional quantitative methods for chaotic systems investigation. It is shown that the relative specific volume possesses the best correlation with the change of attractors among all considered metrics. The proposed approach can be used to study hidden oscillations in experimental data as well.