arXiv subjects

Shigefumi Hata

Publications and source records attributed to Shigefumi Hata.

12 recordsLinked to original sources

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

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↗

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

Synchronization facilitated by frequency differences: Dynamics of coupled-oscillator systems with damaged elements

This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the system is composed of both limit-cycle oscillators and damped oscillators. In this system, as is commonly observed in conventional coupled limit-cycle oscillators, synchronization among oscillators is destroyed when the difference between the natural frequencies of the oscillators increases. However, in the presence of damped oscillators, synchronization can be facilitated by further increasing the frequency difference from the desynchronization state. We conduct numerical simulations on coupled Stuart-Landau oscillators and investigate this reentrance of synchronization systematically. We also propose an approximate theory to predict the stability of the synchronization state based on a linear stability analysis of the fixed point, which reveals the appearance of the Hopf modes. Using this theory, we argue that the reentrance of synchronization driven by increasing frequency differences can be observed in a wide range of coupled-oscillator systems with damaged elements.

nlin.AO↗

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↗

arXiv2023

Higher-order interactions induce anomalous transitions to synchrony

We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase reduction. Our study indicates that higher-order interactions induce anomalous transitions to synchrony. Unlike the conventional Kuramoto model, higher-order interactions lead to anomalous phenomena such as multistability of full synchronization, incoherent, and two-cluster states, and transitions to synchrony through slow switching and clustering. Phase diagrams of the dynamical regimes are constructed theoretically and verified by direct numerical simulations. We also show that similar transition scenarios are observed even if a small heterogeneity in the oscillators' frequency is included.

nlin.AO↗

arXiv2014

Pattern formation in multiplex networks

The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the classical continuous media. Here we study pattern formation in a new framework, namely multiplex networks. These are systems where activator and inhibitor species occupy separate nodes in different layers. Species react across layers but diffuse only within their own layer of distinct network topology. This multiplicity generates heterogeneous patterns with significant differences from those observed in single-layer networks. Remarkably, diffusion-induced instability can occur even if the two species have the same mobility rates; condition which can never destabilize single-layer networks. The instability condition is revealed using perturbation theory and expressed by a combination of degrees in the different layers. Our theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.

nlin.AO↗

arXiv2013

Advection of passive particles over flow networks

The problem of stochastic advection of passive particles by circulating conserved flows on networks is formulated and investigated. The particles undergo transitions between the nodes with the transition rates determined by the flows passing through the links. Such stochastic advection processes lead to mixing of particles in the network and, in the final equilibrium state, concentration of particles in all nodes become equal. As we find, equilibration begins in the subset of nodes, representing flow hubs, and extends to the periphery nodes with weak flows. This behavior is related to the effect of localization of the eigenvectors of the advection matrix for considered networks. Applications of the results to problems involving spreading of infections or pollutants by traffic networks are discussed.

cond-mat.stat-mech↗

arXiv2013

Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks

As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally heterogeneous patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and also called the wave bifurcation, is rare for chemical systems. Here, we extend the analysis by Turing to general networks and apply it to ecological metapopulations of biological species with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of some species, even though they are absent for isolated populations. Furthermore, our theoretical analysis reveals that this instability is more common in ecological metapopulations than in chemical reactions. Indeed, we find the instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Therefore, we suggest that the oscillatory Turing instability is generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.

nlin.PS↗

arXiv2013

Sufficient conditions for wave instability in three-component reaction-diffusion systems

Sufficient conditions for the wave instability in general three-component reaction-diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to determine whether the wave instability can be observed as the mobility of one of the species is gradually increased. It is found that the instability can also occur if one of the three species does not diffuse. Our results provide a useful criterion for searching wave instabilities in reaction-diffusion systems of various origins.

nlin.PS↗

arXiv2011

Optimal phase response curves for stochastic synchronization of limit-cycle oscillators by common Poisson noise

We consider optimization of phase response curves for stochastic synchronization of non-interacting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional shape for sufficiently weak signals is sinusoidal, but can differ for stronger signals. By solving the Euler-Lagrange equation associated with the minimization of the Lyapunov exponent characterizing synchronization efficiency, the optimal phase response curve is obtained. We show that the optimal shape mutates from a sinusoid to a sawtooth as the constraint on its squared amplitude is varied.

nlin.AO↗

arXiv2010

Synchronization of uncoupled oscillators by common gamma impulses: from phase locking to noise-induced synchronization

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by Poisson random impulses, but their difference has not been fully quantified. Here we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between regular periodic and random Poisson impulses. Their dynamics are charac- terized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.

nlin.AO↗