arXiv subjects

Ayumi Ozawa

Publications and source records attributed to Ayumi Ozawa.

4 recordsLinked to original sources

arXiv2026

Basin Metamorphosis in Coupled Phase Oscillators

We investigate the global basin structure of twisted states in nearest-neighbor coupled phase oscillators with a common phase shift $α$. As $α$ increases, basin boundaries become progressively more complex, with their fractal dimension growing toward that of the full ambient phase space. We conjecture that the basins eventually become riddled-like as the system approaches the limit $α\to \fracπ{2}$, where the dynamics becomes volume-preserving. We characterize the transient dynamics via the stabilization time of the winding number and demonstrate that it grows with system size. The scaling accelerates at larger phase shifts, transitioning from logarithmic to power-law behavior. We further analyze the dynamical origin of these long transients. Our results demonstrate how a single phase-shift governs fractal basin complexity and provide new insights into the global geometry and transient dynamics of multistable, yet non-chaotic, coupled phase oscillators.

nlin.CD↗

arXiv2025

Phase reduction of reaction-diffusion systems with delay

We develop a phase reduction method for reaction-diffusion systems with a discrete delay. On the basis of the recent developments in the phase reduction theory for infinite-dimensional systems, we introduce a bilinear form tailored to spatially extended systems involving a discrete delay. By solving the adjoint equation associated with the bilinear form, we obtain the phase sensitivity function, which quantifies the shift of the phase in response to a given perturbation. The theory is verified numerically with the use of the Schnakenberg system with a discrete delay in one spatial dimension. We further demonstrate the utility of the theory by optimizing the interaction between a pair of the Schnakenberg systems, with the use of the phase equation, for maximizing the stability of in-phase synchronization. This study serves as a step towards establishing a theory for analyzing oscillatory systems that involve both spatial degrees of freedom and delay.

nlin.AO↗

arXiv2024

Two distinct transitions in a population of coupled oscillators with turnover: desynchronization and stochastic oscillation quenching

Synchronization, which is caused by mutual coupling, and turnover, which is the replacement of old components with new ones, are observed in various open systems consisting of many components. Although these phenomena can co-occur, the interplay of coupling and turnover has been overlooked. Here, we analyze coupled phase oscillators with turnover and reveal that two distinct transitions occur, depending on both coupling and turnover: desynchronization and what we name stochastic oscillation quenching. Importantly, the latter requires both the turnover and coupling to be sufficiently intense.

nlin.AO↗

arXiv2021

Feedback-induced desynchronization and oscillation quenching in a population of globally coupled oscillators

Motivated from a wide range of applications, various methods to control synchronization in coupled oscillators have been proposed. Previous studies have demonstrated that global feedback typically induces three macroscopic behaviors: synchronization, desynchronization, and oscillation quenching. However, analyzing all of these transitions within a single theoretical framework is difficult, and thus the feedback effect is only partially understood in each framework. Herein, we analyze a model of globally coupled phase oscillators exposed to global feedback, which shows all of the typical macroscopic dynamical states. Analytical tractability of the model enables us to obtain detailed phase diagrams where transitions and bistabilities between different macroscopic states are identified. Additionally, we propose strategies to steer the oscillators into targeted states with minimal feedback strength. Our study provides a useful overview of the effect of global feedback and is expected to serve as a benchmark when more sophisticated feedback needs to be designed.

nlin.AO↗