arXiv subjects

Yuzuru Mitsui

Publications and source records attributed to Yuzuru Mitsui.

5 recordsLinked to original sources

arXiv2026

From phase synchronization to waveform proportionality in a population of R\"ossler oscillators driven by an external pacemaker

The dynamical order of self-sustained oscillators is often characterized by phase synchronization, extensively studied within the framework of the Kuramoto model. It has recently been reported that strong coupling leads to further organization of coupled oscillators, termed waveform proportionality (WP), through amplitude dynamics that cannot be addressed using the Kuramoto model. A previous study [Phys. Rev. Lett. 134, 167202 (2025)] showed that, in coupled oscillator systems, synchronization induces Taylor's law (TL). Particularly, it demonstrated that strong coupling gives rise to WP, which leads to TL with an exponent 2. The findings suggested that WP requires the individual oscillators constituting the coupled system to possess sufficiently fast intrinsic frequencies. Here, we show that WP and TL with an exponent 2 can be induced by a pacemaker oscillator, regardless of the magnitude of the intrinsic frequencies of the individual oscillators in a population. Specifically, even in a population composed of oscillators with slow intrinsic frequencies, WP and TL with an exponent 2 can be induced by coupling the population to a fast pacemaker. Furthermore, we demonstrate that WP and TL can also be induced in a population of non-self-oscillatory units by coupling them to a pacemaker. These results indicate that WP and TL with an exponent 2 are more universal than previously thought, extending beyond oscillator populations with fast intrinsic dynamics.

nlin.AO↗

arXiv2026

Circadian output network can buffer period variability

Circadian rhythms are biological oscillations that govern 24-hour physiological and behavioral processes across most organisms. Recent bioimaging studies have revealed that even individual cells can exhibit circadian rhythms. The period of cellular oscillations can fluctuate due to molecular noise in the circadian clock machinery. Whether regulatory networks downstream of the clock amplify or attenuate clock-derived period fluctuations remains poorly understood. In this study, we numerically observed period variability in a self-sustained oscillator coupled to an output network. Our numerical calculations demonstrated that a serial pathway does not merely relay timing signals but actively shapes rhythmic reliability. The extent of this reduction depended on parameters of both the clock and output systems. For more complex output networks, the shortest-path length from the core oscillator was a major determinant of increased oscillation precision. This noise-buffering effect saturated in long cascades. These results suggest the existence of an intrinsic precision-enhancing mechanism embedded within circadian output networks.

q-bio.MN↗

arXiv2025

Waveform proportionality and Taylor's law in coupled Lorenz systems

Taylor's law (TL), a power-law relationship between the mean and variance of a quantity, has been observed across diverse scientific disciplines. Despite its ubiquity, the underlying mechanisms responsible for TL are not yet fully elucidated. In particular, the frequent empirical observation of TL with an exponent 2 warrants further investigation. In a previous study [Phys. Rev. Lett. 134, 167202 (2025)], we hypothesized that synchronization contributes to the emergence of TL with an exponent 2. To validate this hypothesis, we employed coupled oscillator models, with each oscillator described by a distinct dynamical system: a food chain model, the R\"ossler system, the Brusselator, and the Lorenz system. Our analytical and numerical results demonstrated that strong coupling leads to a form of synchronization wherein time series become proportional to each other, consequently resulting in TL with an exponent 2. Here, we extend our previous findings for the coupled Lorenz system and provide detailed calculations. Our analytical and numerical results demonstrate that, under strong coupling, waveform proportionality and Taylor's law with an exponent 2 emerge not only in the original Lorenz system but also in the generalized and hyperchaotic Lorenz systems.

nlin.AO↗

arXiv2023

Waveform Proportionality and Taylor's Law Induced by Synchronization of Periodic and Chaotic Oscillators

Taylor's law (TL), the scaling relationship between the mean and variance, has been observed in various fields. However, the underlying reasons why TL is so widely observed, why the exponents of TL are often close to 2, and the relationship between temporal and spatial TLs are not fully understood. Here, using coupled oscillator models, we analytically and numerically demonstrate that synchronization can induce TL. In particular, we show that strong synchronization leads to waveform proportionality, resulting in temporal and spatial TLs with exponent 2. Our study can help infer the existence of synchronization solely from the relationship between the mean and variance.

nlin.AO↗

arXiv2020

Spatial and Temporal Taylor's Law in 1-Dim Chaotic Maps

By using low-dimensional chaos maps, the power law relationship established between the sample mean and variance called Taylor's Law (TL) is studied. In particular, we aim to clarify the relationship between TL from the spatial ensemble (STL) and the temporal ensemble (TTL). Since the spatial ensemble corresponds to independent sampling from a stationary distribution, we confirm that STL is explained by the skewness of the distribution. The difference between TTL and STL is shown to be originated in the temporal correlation of a dynamics. In case of logistic and tent maps, the quadratic relationship in the mean and variance, called Bartlett's law, is found analytically. On the other hand, TTL in the Hassell model can be well explained by the chunk structure of the trajectory, whereas the TTL of the Ricker model have a different mechanism originated from the specific form of the map.

nlin.CD↗