Neuroscience Institute, Georgia State University, 100 Piedmont Ave., Atlanta, Georgia 30303, USA.
Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA.
Chaos. 2021 Sep;31(9):093121. doi: 10.1063/5.0065044.
This study focuses on the qualitative and quantitative characterization of chaotic systems with the use of a symbolic description. We consider two famous systems, Lorenz and Rössler models with their iconic attractors, and demonstrate that with adequately chosen symbolic partition, three measures of complexity, such as the Shannon source entropy, the Lempel-Ziv complexity, and the Markov transition matrix, work remarkably well for characterizing the degree of chaoticity and precise detecting stability windows in the parameter space. The second message of this study is to showcase the utility of symbolic dynamics with the introduction of a fidelity test for reservoir computing for simulating the properties of the chaos in both models' replicas. The results of these measures are validated by the comparison approach based on one-dimensional return maps and the complexity measures.
本研究侧重于使用符号描述对混沌系统进行定性和定量描述。我们考虑了两个著名的系统，即 Lorenz 和 Rössler 模型及其标志性吸引子，并证明了通过适当选择符号分区，三个复杂度度量，如香农源熵、Lempel-Ziv 复杂度和马尔可夫转移矩阵，可以很好地用于描述混沌程度，并在参数空间中精确检测稳定窗口。本研究的第二个信息是展示符号动力学的实用性，引入储层计算的保真度测试来模拟两个模型副本中混沌的特性。这些措施的结果通过基于一维返回映射和复杂度度量的比较方法进行验证。
