83 citations · 260 across the 21 of their papers we have counts for
22 papers
Finite Invariant Sets with Bridging Points in Logistic IFS
Hibiki Kato, Tamotsu Onozaki, Yoshitaka Saiki +1
We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps as simple models of regime-switching dynamical systems. Our pr…
A laminar chaotic saddle within a turbulent attractor
Hibiki Kato, Miki U Kobayashi, Yoshitaka Saiki +1
Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid…
The dynamics of the heterochaos baker maps
Yoshitaka Saiki, Hiroki Takahasi, Kenichiro Yamamoto +1
The heterochaos baker maps are piecewise affine maps of the unit square or cube introduced in [Nonlinearity 34, 2021, 5744--5761], to provide a hands-on, elementary understanding o…
Constructing low-dimensional ordinary differential equations from chaotic time series of high/infinite-dimensional systems using radial function-based regression
Natsuki Tsutsumi, Kengo Nakai, Yoshitaka Saiki
In our previous study (N. Tsutsumi, K. Nakai and Y. Saiki (2022)) we proposed a method of constructing a system of differential equations of chaotic behavior only from observable d…
Characterizing Data Assimilation in Navier-Stokes Turbulence with Transverse Lyapunov Exponents
Masanobu Inubushi, Yoshitaka Saiki, Miki U. Kobayashi +1
Data assimilation (DA) reconstructing small-scale turbulent structures is crucial for forecasting and understanding turbulence. This study proposes a theoretical framework for DA b…
Machine learning prediction of the MJO extends beyond one month
Tamaki Suematsu, Kengo Nakai, Tsuyoshi Yoneda +4
The prediction of the Madden-Julian Oscillation (MJO), a massive tropical weather event with vast global socio-economic impacts, has been infamously difficult with physics-based we…
Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics
Natsuki Tsutsumi, Kengo Nakai, Yoshitaka Saiki
We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estima…
The twisted baker map
Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke
As a model to provide a hands-on, elementary understanding of "vortex dynamics", we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set…
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…
Hausdorff dimension of Cantor intersections and robust heterodimensional cycles for heterochaos horseshoe maps
Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke
As a model to provide a hands-on, elementary understanding of chaotic dynamics in dimension three, we introduce a -open set of diffeomorphisms of having two hors…
Regional Synchronization during Economic Contraction: The Case of the U.S. and Japan
Makoto Muto, Tamotsu Onozaki, Yoshitaka Saiki
Two decades of studies have found significant regional differences in the timing of transitions in national business cycles and their durations. Earlier studies partly detect regio…
Synchronization analysis between exchange rates on the basis of purchasing power parity using the Hilbert transform
Makoto Muto, Yoshitaka Saiki
Synchronization is a phenomenon in which a pair of fluctuations adjust their rhythms when interacting with each other. We measure the degree of synchronization between the U.S. dol…
Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable
Kengo Nakai, Yoshitaka Saiki
We construct a data-driven dynamical system model for a macroscopic variable the Reynolds number of a high-dimensionally chaotic fluid flow by training its scalar time-series data.…
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…
Piecewise-linear maps with heterogeneous chaos
Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between t…
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…
Quantitative Quasiperiodicity
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander +1
The Birkhoff Ergodic Theorem concludes that time averages, i.e., Birkhoff averages, of a function along a length ergodic trajectory of a fu…
Measuring quasiperiodicity
Suddhasattwa Das, Chris B. Dock, Yoshitaka Saiki +4
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently s…
Quantitative Quasiperiodicity
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander +1
The Birkhoff Ergodic Theorem concludes that time averages, that is, Birkhoff averages, of a function along an ergodic trajectory of a function …