arXiv subjects

Hiroya Nakao

Publications and source records attributed to Hiroya Nakao.

At least 19 recordsLinked to original sources

arXiv2026

Higher-order interactions for controlling time-delayed Kuramoto model

We propose a framework for controlling the collective dynamics of the time-delayed Kuramoto model based on a delay-free, higher-order approximation of the delayed interactions. By applying the Ott--Antonsen ansatz and the second-order averaging method to the resulting higher-order Kuramoto model, we obtain a one-dimensional reduced equation for the order parameter dynamics. Numerical simulations demonstrate that the higher-order approximation predicts the dynamics of the original delayed system more accurately than the conventional pairwise approximation and enables the realization of bistability and intermediate synchronization states. Our results demonstrate the effectiveness of higher-order interpretations of time delays for the control of oscillator networks with time-delayed interactions.

nlin.AO↗

arXiv2026

Data-driven oscillator model for multi-frequency turbulent flows

The complex dynamics of high-dimensional oscillatory flows can be simplified using phase-reduction analysis, providing a deeper understanding of the flow response to external perturbations. Although phase-based modeling and analysis have been utilized in recent studies on oscillatory fluid flows, their usages are still limited to single-frequency flows due to difficulties in addressing chaotic characteristics induced by multiple frequencies of turbulent flows. In order to overcome this limitation, we propose a data-driven framework that models the dynamics of multi-frequency turbulent flows based on a set of oscillators. The representative oscillators are extracted from the flow field data by training specially designed autoencoders. The oscillator dynamics are modeled through a machine-learning technique using neural networks to accurately predict the multi-frequency oscillatory behavior of turbulent flows. We verify the oscillator-based model of the multi-frequency turbulent flow by applying the proposed data-driven method to the three-dimensional supersonic turbulent flow over a cavity. We show that the extracted oscillators represent the dominant large-scale flow features and reflect the physical characteristics of the turbulent cavity flow. The data-driven oscillator dynamics model accurately forecasts the oscillatory behavior of the turbulent cavity flow for a long period. The proposed data-driven method for reduced-order modeling of turbulent flows with oscillators will enable deeper investigations of perturbation dynamics and control of turbulent flows.

physics.flu-dyn↗

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↗

arXiv2026

Optimal Control for Steady Circulation of a Diffusion Process via Spectral Decomposition of Fokker-Planck Equation

We present a formulation of an optimal control problem for a two-dimensional diffusion process governed by a Fokker-Planck equation to achieve a nonequilibrium steady state with a desired circulation while accelerating convergence toward the stationary distribution. To achieve the control objective, we introduce costs for both the probability density function and flux rotation to the objective functional. We formulate the optimal control problem through dimensionality reduction of the Fokker-Planck equation via eigenfunction expansion, which requires a low-computational cost. We demonstrate that the proposed optimal control achieves the desired circulation while accelerating convergence to the stationary distribution through numerical simulations.

eess.SY↗

arXiv2026

Global Phase Synchronization Decoupled from Amplitude Dynamics

The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models that globally preserve Kuramoto-type phase dynamics by using phase-amplitude coordinates defined via Koopman operator theory. We introduce a solvable model, termed Kuramoto-Stuart-Landau model, which exhibits nontrivial synchronized dynamics far from the limit cycle. We also construct three phase synchronized oscillators whose amplitudes exhibit Lorenz-type chaos. Our method is applicable to general limit-cycle systems, achieving phase synchronization globally while preserving arbitrarily complex amplitude dynamics.

nlin.AO↗

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↗

arXiv2025

Quantum spin van der Pol oscillator -- a spin-based limit-cycle oscillator exhibiting quantum synchronization

We introduce a quantum spin van der Pol (vdP) oscillator as a prototypical model of quantum spinbased limit-cycle oscillators, which coincides with the quantum optical vdP oscillator in the high-spin limit. The system is described as a noisy limit-cycle oscillator in the semiclassical regime at large spin numbers, exhibiting frequency entrainment to a periodic drive. Even in the smallest spin-1 case, mutual synchronization, Arnold tongues, and entanglement tongues in two dissipatively coupled oscillators, and collective synchronization in all-to-all coupled oscillators are clearly observed. The proposed quantum spin vdP oscillator will provide a useful platform for analyzing quantum spin synchronization.

nlin.AO↗

arXiv2025

Manipulating Collective Opinion through Social Network Intervention

Social media platforms have transformed the dynamics of collective opinion formation, enabling rapid, large-scale interactions while simultaneously exposing online discourse to polarization and manipulation. Traditional models of opinion dynamics often predict convergence to a consensus, yet empirical evidence consistently highlights persistent polarization and radicalization, especially on contentious issues. This paper analytically investigates a mathematical model that captures the complex interplay of polarization, radicalization, and consensus within networked societies. By analyzing the emergence and stability of opinion clusters, we identify critical thresholds marking phase transitions in collective behavior, interpreted via a stability landscape. We further explore network-based interventions to manipulate the collective opinion, revealing that reducing inter-agent interactions can lead to unintended, irreversible shifts in opinion distributions. Our results underscore the dual-edged nature of intervention strategies, offering theoretical insight into the fragility and manipulability of public opinion in digital environments.

physics.soc-ph↗

arXiv2025

Time delay embeddings to characterize the timbre of musical instruments using Topological Data Analysis: a study on synthetic and real data

Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning, often overlook subtle characteristics of sound. Topological Data Analysis (TDA) can capture complex patterns, but its application to timbre has been limited, partly because it is unclear how to represent sound effectively for TDA. In this study, we investigate how different time delay embeddings affect TDA results. Using both synthetic and real audio signals, we identify time delays that enhance the detection of harmonic structures. Our findings show that specific delays, related to fractions of the fundamental period, allow TDA to reveal key harmonic features and distinguish between integer and non-integer harmonics. The method is effective for synthetic and real musical instrument sounds and opens the way for future works, which could extend it to more complex sounds using higher-dimensional embeddings and additional persistence statistics.

cs.SD↗

arXiv2025

Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks

The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex networks, allowing for both reciprocal or non-reciprocal links. The emergence of synchronization can be deduced by proving the linear stability of the limit cycle solution for the Stuart-Landau model; the linear coupling assumption allows for a complete analytical treatment of the problem, mostly because the linearized system turns out to be autonomous. In this work, we analyze Stuart-Landau oscillators coupled through nonlinear functions on both undirected and directed networks; synchronization now depends on the study of a non-autonomous linear system and thus novel tools are required to tackle the problem. We provide a complete analytical description of the system for some choices of the nonlinear coupling, e.g., in the resonant case. Otherwise, we develop a semi-analytical framework based on Jacobi-Anger expansion and Floquet theory, which allows us to derive precise conditions for the emergence of complete synchronization. The obtained results extend the classical theory of coupled oscillators and pave the way for future studies of nonlinear interactions in networks of oscillators and beyond.

nlin.PS↗

arXiv2025

Optimal interaction functions realizing higher-order Kuramoto dynamics with arbitrary limit-cycle oscillators

The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators are derived from weakly interacting limit-cycle oscillators via phase reduction, this procedure does not necessarily yield the Kuramoto model or its higher-order extensions exactly for general limit-cycle oscillators and interaction functions, except in the special case of interacting Stuart-Landau oscillators. In this study, we artificially design optimal pairwise and higher-order interaction functions between limit-cycle oscillators, from which higher-order Kuramoto models can be exactly derived via phase reduction for arbitrary smooth limit-cycle oscillators. We validate the results through numerical simulations of FitzHugh-Nagumo oscillators, demonstrating that the collective synchronization dynamics predicted by the reduced higher-order Kuramoto models are realized. Control of the collective phase of the FitzHugh-Nagumo oscillators based on Ott-Antonsen reduction of the higher-order Kuramoto model is also demonstrated.

nlin.AO↗

arXiv2025

Data-driven phase control for limit-cycle oscillators under partial observation

Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase variable, is useful for analyzing the oscillator dynamics. In the control of limit-cycle oscillators with unknown dynamics, the oscillator phase should be estimated from time series under partial observation in real time. In this study, we present an autoencoder-based method for estimating the oscillator phase using delay embedding of observed state variables. We evaluate the order of the phase estimation error under weak inputs and apply the method to phase-reduction-based feedback control of mutual synchronization of two oscillators under partial observation. The effectiveness of our method is illustrated by numerical examples using two types of limit-cycle oscillators, the Stuart-Landau and Hodgkin-Huxley models.

nlin.AO↗

arXiv2025

When higher-order interactions enhance synchronization: the case of the Kuramoto model

Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled oscillators, traditionally assuming pairwise interactions. However, many real-world systems exhibit group and many-body interactions, which can be effectively modeled through hypergraphs. Here we show that the effect of such higher-order interactions on synchronization is non-monotonic. Through a numerical study of higher-order Kuramoto models on random hypergraphs and on globally coupled systems, we find that the degree of synchronization reached from incoherent initial conditions is maximized at a small but nonzero higher-order coupling strength: weak higher-order interactions enhance synchronization when added to pairwise ones, whereas strong ones work against it, in line with earlier reports of reduced basins and of cluster states. We further show, through a cost-constrained allocation analysis, that under a constrained budget for interactions a mixed allocation of pairwise and higher-order couplings consistently achieves higher synchronization than relying on either type alone. These findings clarify the role of higher-order interactions in shaping collective dynamics and point to design principles for optimizing synchronization in complex systems.

nlin.AO↗

arXiv2025

Dynamic mode decomposition for detecting oscillatory transient activity via sparsity and smoothness regularization

Dynamic mode decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with a single frequency and a growth rate, DMD enables a natural modal decomposition and dimensionality reduction of complex dynamical systems. However, when DMD is applied to transient dynamics, even if a large number of modes are used, it remains difficult to interpret how these modes contribute to the transient behavior. In this study, we propose a simple extension of DMD that facilitates extraction of oscillatory transient activity by introducing time-varying amplitudes for the DMD modes based on sparsity and smoothness regularization. This approach enables identification of dynamically significant modes and extraction of their transient activities, providing a more interpretable representation of non-steady dynamics. We illustrate the validity of the proposed method using a simple example and then apply it to fluid flow data of a laminar airfoil wake exhibiting transient behavior. We demonstrate that it can capture the temporal structure of mode activations that are not accessible with the standard DMD method.

physics.flu-dyn↗

arXiv2025

Theory of phase reduction from hypergraphs to simplicial complexes: a general route to higher-order Kuramoto models

Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such as the Kuramoto model. Classically, the method has been applied in the case where the interactions are only pairwise (two-body). However, increasing evidence shows that interactions in real-world systems are not pairwise but higher-order, i.e., many-body. Although synchronization in higher-order systems has received much attention, analytical results are scarce because of the highly nonlinear nature of the framework. In this paper, we fill the gap by presenting a general theory of phase reduction for the case of higher-order interactions. We show that the higher-order topology is preserved in the phase reduced model at the first order and that only odd couplings have an effect on the dynamics when certain symmetries are present. Additionally, we show the power and ductility of the phase reduction approach by applying it to a population of Stuart-Landau oscillators with an all-to-all configuration and with a ring-like hypergraph topology; in both cases, only the analysis of the phase model can provide insights and analytical results.

nlin.AO↗

arXiv2025

Synchronization of Dirac-Bianconi driven oscillators

In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network theory addresses this by considering variables defined on nodes, links, triangles, and higher-order simplices, called topological signals (or cochains). Moreover, topological signals of different dimensions can interact through the Dirac-Bianconi operator, which allows coupling between topological signals defined, for example, on nodes and links. Such interactions can induce various dynamical behaviors, for example, periodic oscillations. The oscillating system consists of topological signals on nodes and links whose dynamics are driven by the Dirac-Bianconi coupling, hence, which we call it Dirac-Bianconi driven oscillator. Using the phase reduction method, we obtain a phase description of this system and apply it to the study of synchronization between two such oscillators. This approach offers a way to analyze oscillatory behaviors in higher-order networks beyond the node-based paradigm, while providing a ductile modeling tool for node- and edge-signals.

nlin.PS↗

arXiv2025

Flutter Suppression Enhancement in Coupled Nonlinear Airfoils with Intermittent Mixed Interactions

Flutter suppression facilitates the improvement of structural reliability to ensure the flight safety of an aircraft. In this study, we propose a novel strategy for enlarging amplitude death (AD) regime to enhance flutter suppression in two coupled identical airfoils with structural nonlinearity. Specifically, we introduce an intermittent mixed coupling strategy, i.e., a linear combination of intermittent instantaneous coupling and intermittent time-delayed coupling between two airfoils. Numerical simulations are performed to reveal the influence mechanisms of different coupling scenarios on the dynamical behaviors of the coupled airfoil systems. The obtained results indicate that the coupled airfoil systems experience the expected AD behaviors within a certain range of the coupling strength and time-delayed parameters. The continuous mixed coupling favors the onset of AD over a larger parameter set of coupling strength than the continuous purely time-delayed coupling. Moreover, the presence of intermittent interactions can lead to a further enlargement of the AD regions, that is, flutter suppression enhancement. Our findings support the structural design and optimization of an aircraft wing for mitigating the unwanted aeroelastic instability behaviors.

nlin.CD↗