Calculating Persistence Homology of Attractors in High-Dimensional Chaotic Systems

While persistent homology is a basic but useful tool for describing the topological features of spaces, it has rarely been applied to describe the chaotic attractor whose shape could be very intriguing and complex. Especially for high-dimensional chaotic attractors, on one hand it reveals the evolution and stability of dynamical systems yet on the other hand, since it is a natural restriction for human researchers that they are unable to see more than three dimensionalities, methods for categorizing high dimensional attractors are lacking. Therefore, in this article we propose the method of applying persistent homology calculation to high-dimensional chaotic attractors and give several representative examples from different genres of chaotic systems for whose topological structure being displayed.