Physics Department, Boğaziçi University, 34342 Istanbul, Turkey.
IST Austria, 3400 Klosterneuburg, Austria.
Chaos. 2020 Mar;30(3):033109. doi: 10.1063/1.5122969.
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent homology for the characterization of state space projections of chaotic trajectories and periodic orbits. By comparing the shapes along a chaotic trajectory to those of the periodic orbits, state space persistence analysis quantifies the shape similarity of chaotic trajectory segments and periodic orbits. We demonstrate the method by applying it to the three-dimensional Rössler system and a 30-dimensional discretization of the Kuramoto-Sivashinsky partial differential equation in (1+1) dimensions.
我们介绍了“状态空间持续分析”，用于推断从高维混沌吸引子中获得的时间序列数据的符号动力学。为此，我们采用了一种称为持久同调的拓扑数据分析技术，用于描述混沌轨迹和周期轨道的状态空间投影。通过将混沌轨迹的形状与周期轨道的形状进行比较，状态空间持续分析量化了混沌轨迹段和周期轨道的形状相似性。我们通过将其应用于三维 Rössler 系统和（1+1）维的 Kuramoto-Sivashinsky 偏微分方程的 30 维离散化来演示该方法。
