arXiv subjects

Hiroshi Kori

Publications and source records attributed to Hiroshi Kori.

At least 19 recordsLinked to original sources

arXiv2026

Criticality of nonreciprocal phase oscillators with long-range interactions

We study noisy identical Kuramoto-Sakaguchi oscillators with phase lag $α\in[0,π/2)$, where $α>0$ induces nonreciprocal interactions. Numerical phase diagrams in the $(σ, α)$ plane in fully-connected graphs, formed by long-range weights tuned by $σ$ on $d$-dimensional lattices, reveal a critical phase lag $α_c$, below which spontaneous synchronization occurs. This critical phase lag decreases monotonically with $σ$. We characterize the critical behavior analytically using the dynamical renormalization group theory.

nlin.AO↗

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↗

arXiv2026

An Isochron-Free Framework for Phase Reduction and Coupling Inference

Phase description provides a compact and powerful framework for analyzing synchronization dynamics in weakly coupled limit-cycle oscillators. While its classical formulation relies on the asymptotic phase defined by isochrons, reconstructing isochrons from observed trajectories is often challenging for complex models and real-world systems. Here we develop an isochron-free framework based on a readily computable generalized phase, such as the polar angle computed from observed trajectories. We theoretically show that, under near-uniform rotation of the generalized phase and sufficiently stable amplitude dynamics, a one-period stroboscopic description yields a closed circle map. The interaction term of the resulting circle map coincides, to leading order, with the phase coupling function obtained from the conventional phase reduction. Based on this circle map, we propose a method to infer coupling from oscillatory time series. The method is validated using synthetic data from van der Pol oscillators. Our framework broadens the applicability of phase reduction and provides a theoretically grounded method for coupling inference from oscillatory data.

nlin.AO↗

arXiv2026

From phase synchronization to waveform proportionality in a population of Rössler 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

Uncertainty-Aware Sparse Identification of Dynamical Systems via Bayesian Model Averaging

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point estimates alone can be misleading, because multiple model components may explain the observed data comparably well, especially when the data are limited or the dynamics exhibit poor identifiability. Quantifying the uncertainty associated with model selection is therefore essential for constructing reliable dynamical models from data. In this work, we develop a Bayesian sparse identification framework for dynamical systems with coupled components, aimed at inferring both interaction structure and functional form together with principled uncertainty quantification. The proposed method combines sparse modeling with Bayesian model averaging, yielding posterior inclusion probabilities that quantify the credibility of each candidate interaction and basis component. Through numerical experiments on oscillator networks, we show that the framework accurately recovers sparse interaction structures with quantified uncertainty, including higher-order harmonic components, phase-lag effects, and multi-body interactions. We also demonstrate that, even in a phenomenological setting where the true governing equations are not contained in the assumed model class, the method can identify effective functional components with quantified uncertainty. These results highlight the importance of Bayesian uncertainty quantification in data-driven discovery of dynamical models.

stat.AP↗

arXiv2026

Distinguishing pairwise and higher-order interactions in coupled oscillators from time series

Rhythmic phenomena, which are ubiquitous in biological systems, are typically modelled as systems of coupled limit cycle oscillators. Recently, there has been an increased interest in understanding the impact of higher-order interactions on the population dynamics of coupled oscillators. Meanwhile, the estimation of a mathematical model from experimental data is an essential step in understanding the dynamics of real-world complex systems. In coupled oscillator systems, identifying the type of interaction (e.g. pairwise or three-body) is challenging, because different interactions can exhibit similar dynamical states in experimental conditions. In this study, we have developed a method based on the adaptive LASSO (Least Absolute Shrinkage and Selection Operator) to infer the interactions among oscillators from time series data. The proposed method successfully identifies the type of interaction and estimates the probabilities of pairwise and three-body couplings. Through systematic analysis of synthetic datasets, we have demonstrated that our method outperforms two baseline methods, LASSO and OLS (Ordinary Least Squares), in accurately inferring the topology and strength of couplings between oscillators. Furthermore, the proposed method is applied to human brain network data, demonstrating its practical utility. Finally, we extend the method to more general oscillatory systems, including those exhibiting the deformation of limit cycles and those with four-body interactions. These results suggest that our method is a promising tool for identifying interaction mechanisms in oscillatory systems.

nlin.CD↗

arXiv2026

Multistability and Control in Ring Networks of Phase Oscillators with Frequency Heterogeneity and Phase Lag

Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states with different wavenumbers are simultaneously stable. This model is an extension of the one studied in detail in previous studies by introducing inhomogeneities in the natural frequencies and the phase lag in the interaction, which are essential factors in the application. We investigate basin size distribution, which characterizes the size of the initial value set that converges to each synchronous state, showing that the basin size of synchronous states with higher wave-numbers broadens as the phase lag increases up to a certain extent. Weak inhomogeneities in the natural frequencies are also found to broaden the basin size of synchronous states with lower wave-numbers, i.e., more synchronous states. The latter result is seemingly counter-intuitive, but occurs because the higher wavenumber states are more vulnerable to inhomogeneity. Finally, we propose a control method that exploits inhomogeneity and phase lag to steer the system into a synchronized state with a specific wavenumber. This research furthers our understanding of the design principles and control of oscillator networks.

nlin.AO↗

arXiv2026

Qualitatively distinct mechanisms of noise-induced escape in diffusively coupled bistable elements

The analysis of noise-induced escape in populations of bistable elements is challenging, because nonlinearity, coupling, and noise all play essential roles. We show that the interplay of these three factors yields three qualitatively distinct escape mechanisms depending on coupling strength in populations of diffusively coupled bistable elements. To clarify dominant driving factors of escape dynamics, we develop a model-reduction approach, deriving three effective one-dimensional dynamics: nonlinear mean-field Fokker-Planck equation in the weak-coupling regime, stochastic mean-field dynamics in the strong-coupling regime, and deterministic mean-field dynamics in the intermediate regime. We validate these reduced descriptions by comparing predicted mean escape times with numerical simulations. We identify a distinct dominant driving factor of collective escape in each regime. Notably, the three mechanisms emerge through the interplay of nonlinearity, diffusive coupling, and dynamical noise -- rather than bifurcations of the noise-free system. Our approach serves as a framework applicable to other stochastic nonlinear systems with diffusive coupling, motivating a further search for similar synergistic phenomena.

nlin.AO↗

arXiv2026

Degree heterogeneity shapes escape mechanisms in networks of diffusively coupled bistable elements

For fully connected populations of diffusively coupled bistable elements, we identified three qualitatively distinct mechanisms of noise-induced escape as coupling strength varies [H. Ishii and H. Kori, arXiv:2512.01388 (2025)]. Here we generalize these results to a class of networked systems and demonstrate that degree heterogeneity (i.e., variability in node degree) shapes escape mechanisms alongside coupling strength. In applied contexts, networks of noisy bistable elements provide a minimal conceptual framework for understanding abrupt state transitions in complex systems. Theoretically, a quantitative approach to escape is challenging because nonlinearity, network interactions, and dynamical noise jointly shape the collective dynamics. We extend the analytical framework developed for the fully connected model to a class of networked systems based on the annealed network approximation. We derive three effective one-dimensional descriptions of collective escape dynamics. We validate our theoretical predictions for mean escape times by direct numerical simulations. Our analysis reveals that the validity and quantitative behavior of the reduced descriptions depend on degree heterogeneity in addition to coupling strength. This work extends the classification of escape mechanisms to networked bistable elements. Furthermore, our analytical framework provides tools for understanding synergistic phenomena arising from the interplay of nonlinearity, diffusive coupling, and dynamical noise.

nlin.AO↗

arXiv2026

Inferring Coupled Stuart-Landau Equations from Waveforms

We present a data-driven framework to infer phase-amplitude equations of coupled limit-cycle oscillators directly from waveform measurements. Exploiting the universality of the Stuart-Landau normal form near a supercritical Hopf bifurcation, we reconstruct a near-identity transformation from two independent observables of an isolated oscillator and infer the intrinsic Stuart-Landau parameters. Using this reconstructed transformation, we then estimate linear coupling coefficients from paired measurements. The method accurately recovers parameters for coupled van der Pol oscillators, providing a quantitative benchmark. Applied to a high-dimensional hydrodynamic system of two coupled collapsible-channel oscillators, the inferred Stuart-Landau model captures bistability between in-phase and anti-phase synchronization and reveals that the anti-phase state is destabilized through a Neimark-Sacker bifurcation. Our approach enables quantitative prediction of synchronization transitions involving amplitude dynamics from experimentally accessible waveform data.

nlin.AO↗

arXiv2025

Network inference applicable to both synchronous and desynchronous systems from oscillatory signals

Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand and control synchronization dynamics in the real world, it is essential to identify the network from the observed data. While previous studies have developed the methods for inferring the network of asynchronous systems, it remains challenging to infer the network of well-synchronized oscillators. In this study, we develop a method for inferring the network of synchronized and desynchronized oscillators from time series. Our method expands the applicability of network inference to a wider class of oscillatory systems. The proposed method discards a large part of data used for inference, which may seem counterintuitive. However, the effectiveness of the method is supported by the phase reduction theory, a well-established theory for weakly coupled oscillators. We verify the proposed method by applying it to simulated data of the limit-cycle oscillators. This study provides an important step towards understanding synchronization in real-world systems from a network perspective.

nlin.AO↗

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 Rössler 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↗

arXiv2025

Bayesian estimation of coupling strength and heterogeneity in a coupled oscillator model from macroscopic quantities

Various macroscopic oscillations, such as the heartbeat and the flashing of fireflies, are created by synchronizing oscillatory units (oscillators). To elucidate the mechanism of synchronization, several coupled oscillator models have been devised and extensively analyzed. Although parameter estimation of these models has also been actively investigated, most of the proposed methods are based on the data from individual oscillators, not from macroscopic quantities. In the present study, we propose a Bayesian framework to estimate the model parameters of coupled oscillator models, using the time series data of the Kuramoto order parameter as the only given data. We adopt the exchange Monte Carlo method for the efficient estimation of the posterior distribution and marginal likelihood. Numerical experiments are performed to confirm the validity of our method and examine the dependence of the estimation error on the observational noise and system size.

physics.data-an↗

arXiv2025

Uncovering influence of football players' behaviour on team performance in ball possession through dynamical modelling

A quest for uncovering influence of behaviour on team performance involves understanding individual behaviour, interactions with others and environment, variations across groups, and effects of interventions. Although insights into each of these areas have accumulated in sports science literature on football, it remains unclear how one can enhance team performance. We analyse influence of football players' behaviour on team performance in three-versus-one ball possession game by constructing and analysing a dynamical model. We developed a model for the motion of the players and the ball, which mathematically represented our hypotheses on players' behaviour and interactions. The model's plausibility was examined by comparing simulated outcomes with our experimental result. Possible influences of interventions were analysed through sensitivity analysis, where causal effects of several aspects of behaviour such as pass speed and accuracy were found. Our research highlights the potential of dynamical modelling for uncovering influence of behaviour on team effectiveness.

physics.soc-ph↗

arXiv2025

Nonequilibrium thermodynamics of populations of weakly-coupled low-temperature-differential Stirling engines with synchronous and asynchronous transitions

This study developed the theory of nonequilibrium thermodynamics for populations of low-temperature-differential (LTD) Stirling engines weakly-coupled in a general class of networks to clarify the effects of synchronous and asynchronous transitions on the power and thermal efficiency. We first show that synchronous (asynchronous) transitions increase (decrease) the power and thermal efficiency of weakly-coupled LTD Stirling engines based on quasilinear response relations between formally defined thermodynamic fluxes and forces. After that, we construct a conceptual model satisfying the quasilinear response relations to give a physical interpretation of the changes in power and thermal efficiency due to synchronous and asynchronous transitions, and justify the use of this conceptual model. We then show that the conceptual model, rather than the quasilinear response relations, preserves the thermodynamic irreversibility of the original model and thus gives more accurate results than those using the quasilinear response relations. Finally, we compare the dynamics between the original and the conceptual models for two-engine systems and show that the conceptual models roughly preserve the dynamical characteristics leading up to the synchronous transitions, while some detailed dynamical structures are lost.

cond-mat.stat-mech↗

arXiv2025

Synchronization and its slow decay in noisy oscillators with simplicial interactions

Previous studies on oscillator populations with two-simplex interaction have reported novel phenomena such as discontinuous desynchronization transitions and multistability of synchronized states. However, the noise effect is not well understood. Here, we study a higher-order network of noisy oscillators with generic interactions consisting of one-simplex and two types of two-simplex interactions. We observe that when a type of two-simplex interaction is dominant, synchrony is eroded and eventually disappears even for infinitesimally weak noise. Nevertheless, synchronized states may persist for extended periods, with the lifetime increasing approximately exponentially with the strength of the two-simplex interaction. When one-simplex or another type of two-simplex interaction is sufficiently strong, noise erosion is prevented, and synchronized states become persistent. A weakly nonlinear analysis reveals that as one-simplex coupling increases, the synchronized state appears supercritically or subscritically, depending on the interaction strength. Furthermore, assuming weak noise and using Kramers' rate theory, we derive a closed dynamical equation for the Kuramoto order parameter, from which the time scale of the erosion process is derived. Our study elucidates the synchronization and desynchronization of oscillator assemblies in higher-order networks and is expected to provide insights into such systems' design and control principles.

nlin.AO↗

arXiv2024

Forecasting the Forced van der Pol Equation with Frequent Phase Shifts Using Reservoir Computing

We tested the performance of reservoir computing (RC) in predicting the dynamics of a certain non-autonomous dynamical system. Specifically, we considered a van del Pol oscillator subjected to periodic external force with frequent phase shifts. The reservoir computer, which was trained and optimized with simulation data generated for a particular phase shift, was designed to predict the oscillation dynamics under periodic external forces with different phase shifts. The results suggest that if the training data have some complexity, it is possible to quantitatively predict the oscillation dynamics exposed to different phase shifts. The setting of this study was motivated by the problem of predicting the state of the circadian rhythm of shift workers and designing a better shift work schedule for each individual. Our results suggest that RC could be exploited for such applications.

nlin.AO↗

arXiv2024

Periodic forces combined with feedback induce quenching in a bistable oscillator

The coexistence of an abnormal rhythm and a normal steady state is often observed in nature (e.g., epilepsy). Such a system is modeled as a bistable oscillator that possesses both a limit cycle and a fixed point. Although bistable oscillators under several perturbations have been addressed in the literature, the mechanism of oscillation quenching, a transition from a limit cycle to a fixed point, has not been fully understood. In this study, we analyze quenching using the extended Stuart-Landau oscillator driven by periodic forces. Numerical simulations suggest that the entrainment to the periodic force induces the amplitude change of a limit cycle. By reducing the system with an averaging method, we investigate the bifurcation structures of the periodically-driven oscillator. We find that oscillation quenching occurs by the homoclinic bifurcation when we use a periodic force combined with quadratic feedback. In conclusion, we develop a state-transition method in a bistable oscillator using periodic forces, which would have the potential for practical applications in controlling and annihilating abnormal oscillations. Moreover, we clarify the rich and diverse bifurcation structures behind periodically-driven bistable oscillators, which we believe would contribute to further understanding the complex behaviors in non-autonomous systems.

nlin.AO↗