Abstract
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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
