6 papers
Dynamical system analysis of a data-driven model constructed by reservoir computing
Miki U Kobayashi, Kengo Nakai, Yoshitaka Saiki +1
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures…
Quasiperiodic orbits in Siegel disks/balls and the Babylonian problem
Yoshitaka Saiki, James A. Yorke
We investigate numerically complex dynamical systems where a fixed point is surrounded by a disk or ball of quasiperiodic orbits, where there is a change of variables (or conjugacy…
Low-dimensional paradigms for high-dimensional hetero-chaos
Yoshitaka Saiki, Miguel A. F. Sanjuan, James A. Yorke
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more d…
Machine-learning inference of fluid variables from data using reservoir computing
Kengo Nakai, Yoshitaka Saiki
We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowl…
The continuous route to multi-chaos
Yoshitaka Saiki, Miguel A. F. Sanjuan, James A. Yorke
For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". I…
Solving the Babylonian Problem of quasiperiodic rotation rates
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander +1
A trajectory is quasiperiodic if the trajectory lies on and is dense in some -dimensional torus, and there is a choice of coordinates on the…