arXiv subjects

Miki U. Kobayashi

Publications and source records attributed to Miki U. Kobayashi.

5 recordsLinked to original sources

arXiv2026

On the attractor in a high-dimensional neural network dynamics of reservoir computing: Lyapunov analysis viewpoint

Recent theoretical developments of reservoir computing have clarified a sufficient condition about which reservoir computing can capture the dynamics of a target system, enabling the reconstruction of dynamical invariants. Even when the condition is relaxed, the reservoir computing is found to succeed in reconstructing time series. In this study, we investigate numerically the dynamical structures underlying the embedding structure by comparing the Lyapunov spectrum of a high-dimensional neural network in a reservoir computing model with that of the actual system. We also compute Lyapunov exponents restricted to the tangent space of the inertial manifold in a high-dimensional neural network. Our results provide numerical evidence that reservoir computing can accurately identify the Lyapunov spectrum of the target system, including all negative exponents.

nlin.CD↗

arXiv2025

Time-delayed feedback control for random dynamical systems

We extend the Pyragas time-delayed feedback control (TDFC) to apply it to random dynamical systems and introduce an extended classification based on Lyapunov exponents and trajectory fluctuations. We demonstrate the applicability of this framework using the random logistic map and the stochastic Rössler system. Our results reveal that noise-induced chaos triggers a transition from stable to unstable regimes based on a phenomenon inherent to random dynamical systems.

nlin.CD↗

arXiv2023

Characterizing Data Assimilation in Navier-Stokes Turbulence with Transverse Lyapunov Exponents

Data assimilation (DA) reconstructing small-scale turbulent structures is crucial for forecasting and understanding turbulence. This study proposes a theoretical framework for DA based on ideas from chaos synchronization, in particular, the transverse Lyapunov exponents (TLEs). The analysis with TLEs characterizes a critical length scale, below which the turbulent dynamics is synchronized to the larger-scale turbulent dynamics, indicating successful DA. An underlying link between TLEs and the maximal Lyapunov exponent suggests that the critical length scale depends on the Reynolds number. Furthermore, we discuss new directions of DA algorithms based on the proposed framework.

physics.flu-dyn↗

arXiv2017

Delay sober up drunkers: Control of diffusion in random walkers

Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic process, i.e., a random walk and observe its diffusion phenomenon with time delayed feedback. Surprisingly, the diffusion coefficient decreases with increasing the delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying the time-delay feedback to a molecular dynamics model.

nlin.CD↗

arXiv2007

Periodic-orbit determination of dynamical correlations in stochastic processes

It is shown that large deviation statistical quantities of the discrete time, finite state Markov process $P_{n+1}^{(j)}=\sum_{k=1}^NH_{jk}P_n^{(k)}$, where P_n^{(j)} is the probability for the j-state at the time step n and H_{jk} is the transition probability, completely coincides with those from the Kalman map corresponding to the above Markov process. Furthermore, it is demonstrated that by using simple examples, time correlation functions in finite state Markov processes can be well described in terms of unstable periodic orbits embedded in the equivalent Kalman maps.

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