arXiv subjects

Keisuke Taga

Publications and source records attributed to Keisuke Taga.

8 recordsLinked to original sources

arXiv2026

Global Analytical Solution of the Identical Kuramoto Model for N=3 via Koopman Eigenfunctions

The Kuramoto model is a paradigmatic model of collective synchronization in coupled oscillator systems. Although its mathematical properties have been extensively investigated, exact phase trajectories from arbitrary initial conditions have been available only for the simplest case, N=2. In this study, we provide a global analytical solution for the phase trajectories of the all-to-all coupled Kuramoto model with identical oscillators for N=3. This solution is obtained by constructing Koopman eigenfunctions that relate the phases to time and reducing the phase dynamics to time-dependent quartic equations. The algebraic branch corresponding to the initial condition is then selected to recover the corresponding phase trajectory. This gives an explicit algebraic reconstruction of the nonlinear phase dynamics from Koopman eigenfunctions.

nlin.AO↗

arXiv2026

Watanabe-Strogatz Invariants in the Liouvillian Dynamics of Coupled Phase Oscillators via the Koopman Framework

In dynamical systems, invariants, i.e., constants of motion conserved along the trajectory, play important roles in characterizing the system's dynamical behavior. Recent applications of the Koopman operator framework to nonlinear dynamical systems have provided new insights into the invariants. For a certain class of globally coupled phase oscillators, which serve as models for various synchronization phenomena, Watanabe and Strogatz proved the existence of N-3 invariants in N oscillator systems. In this study, we derive these invariants from an operator-theoretic perspective by exploiting the relation between Liouvillian (Perron-Frobenius) and Koopman descriptions of the dynamics. Exploiting a simple multiplicative property of functions under the action of the Liouvillian and Koopman operators, we explicitly construct a family of functions whose ratios yield the invariants of the underlying dynamics. Our analysis successfully reproduces the full set of N-3 invariants known in Watanabe-Strogatz theory, and offers an alternative spectral perspective. We demonstrate this approach for a well-studied class of phase models, including the Ermentrout-Kopell, pairwise Kuramoto, and higher-order Kuramoto models.

math.DS↗

arXiv2025

Collective dynamics of higher-order Vicsek model emerging from local conformity interactions

The Vicsek model is the paradigmatic framework for collective motion in systems of self-propelled particles. In its continuous-time formulation and most of its extensions, alignment arises from pairwise interactions among neighboring particles. In this work, we consider a model in which each particle assigns weights to its neighbors according to their alignment with the local consensus. This simple mechanism naturally yields a Vicsek-type model with pairwise and higher-order (i.e., nonpairwise) interactions. We analyze its collective dynamics through numerical simulations and approximate theory in the absence and presence of noise. The higher-order interactions generate a novel bidirectionally ordered phase, in which particles self-organize into oppositely moving groups. Moreover, we show that, depending on the relative strength of the pairwise and three-body interactions, the order-disorder transition can be either continuous or abrupt.

cond-mat.stat-mech↗

arXiv2025

Emergence of higher-order interactions in systems of coupled Kuramoto oscillators with time delay

We show that higher-order interactions naturally emerge from time-delayed pairwise coupling in Kuramoto oscillators. By expanding the delayed pairwise coupling to the second order, we derive a delay-free Kuramoto model possessing both pairwise and three-body interactions. Numerical simulations and stability analysis demonstrate that the three-body Kuramoto model and the time-delayed pairwise Kuramoto model exhibit qualitatively consistent synchronization transitions under appropriate conditions. In particular, the bistability arising in the time-delayed Kuramoto model is accounted for by the three-body interactions. Our findings reveal that time delays can be recast effectively as higher-order interactions, providing an insight into how coupling delays shape collective dynamics.

nlin.AO↗

arXiv2024

Universality in the tape-peeling trace

Spatiotemporal patterns, which are of interest in statistical physics and nonlinear dynamics, form on the tape-peeling trace. Recently, we have proposed a mathematical model to describe these pattern formation in the tape-peeling trace. In this paper, we further investigate the tape-peeling model from the perspective of its universality class. We confirm that our model belongs to the 1-dimensional directed percolation universality class. Furthermore, the experimental results from a previous study are re-analyzed, and it is suggested that the tape-peeling trace can also be classified within the 1-dimensional directed percolation universality class.

cond-mat.stat-mech↗

arXiv2023

Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata

We apply Dynamic Mode Decomposition (DMD) to Elementary Cellular Automata (ECA). Three types of DMD methods are considered and the reproducibility of the system dynamics and Koopman eigenvalues from observed time series are investigated. While standard DMD fails to reproduce the system dynamics and Koopman eigenvalues associated with a given periodic orbit in some cases, Hankel DMD with delay-embedded time series improves reproducibility. However, Hankel DMD can still fail to reproduce all the Koopman eigenvalues in specific cases. We propose an Extended DMD method for ECA that uses nonlinearly transformed time series with discretized Walsh functions and show that it can completely reproduce the dynamics and Koopman eigenvalues. Linear-algebraic backgrounds for the reproducibility of the system dynamics and Koopman eigenvalues are also discussed.

nlin.CG↗

arXiv2023

A tape-peeling model for spatiotemporal pattern formation by deformed adhesives

We propose a new model for pattern formation in peeling of an adhesive tape based on the equation of motion for the displacement of deformed adhesives in the peel front. The spatiotemporal patterns obtained from the model are consistent with those from previous models and experiments. Moreover, dynamical and statistical properties of the patterns are investigated.

nlin.PS↗

arXiv2021

Koopman spectral analysis of elementary cellular automata

We perform a Koopman spectral analysis of elementary cellular automata (ECA). By lifting the system dynamics using a one-hot representation of the system state, we derive a matrix representation of the Koopman operator as a transpose of the adjacency matrix of the state-transition network. The Koopman eigenvalues are either zero or on the unit circle in the complex plane, and the associated Koopman eigenfunctions can be explicitly constructed. From the Koopman eigenvalues, we can judge the reversibility, determine the number of connected components in the state-transition network, evaluate the periods of asymptotic orbits, and derive the conserved quantities for each system. We numerically calculate the Koopman eigenvalues of all rules of ECA on a one-dimensional lattice of 13 cells with periodic boundary conditions. It is shown that the spectral properties of the Koopman operator reflect Wolfram's classification of ECA.

nlin.CG↗