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.

中文翻译：

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检测非平衡系统中的隐藏振荡

近几十年来，具有隐藏吸引子的混沌系统得到了广泛的研究。在这个领域，没有平衡的系统特别有趣。由于多稳态系统可以在几个隐藏的吸引子之间交替，因此很难使用已知的分析技术检测它们的隐藏振荡。在这项研究中，我们建议应用递归分析方法作为解决此问题的可能方法。我们考虑新的量测，称为相对比容，它与吸引子的变化相关。我们选择改进的 Sprott A 系统作为多滚动吸引子的示例来验证所提出的方法。我们将新的递归度量与其他用于混沌系统调查的传统定量方法进行了比较。结果表明，在所有考虑的指标中，相对比容与吸引子变化的相关性最好。所提出的方法也可用于研究实验数据中的隐藏振荡。