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Yoshiyuki Y. Yamaguchi

Publications and source records attributed to Yoshiyuki Y. Yamaguchi.

At least 19 recordsLinked to original sources
arXiv2026

Fluctuation--Response Relation in Finite-Size Noisy Coupled Phase Oscillators

Fluctuation--response relations (FRRs) provide a fundamental relation between spontaneous fluctuations and the linear response to external perturbations, yet their validity in non-equilibrium systems remains an open problem. In a general class of noisy, finite-size, mean-field models of coupled phase oscillators, we reveal two types of FRRs in the incoherent phase below the synchronization transition. The first, corresponding to the infinite-size limit (I-FRR), involves the convolution between the external force and the correlation function in the time domain. The second, the finite-size counterpart (F-FRR), is governed by finite-size fluctuations and carries a correction factor: a spectrum function whose roots correspond to eigenvalues, or Landau poles, of the linear operator. The finite-size fluctuations are suppressed in the weak-coupling or strong-noise limits, and F-FRR reduces to I-FRR. Our analytical findings are verified by extensive numerical simulations.

cond-mat.stat-mech↗
arXiv2026

Conformation dynamics in asymmetric chain-like three-body bead-spring models

We consider conformation dynamics of a chain-like three-body bead-spring model, in which three point masses are connected in series by two springs and the conformation is defined by the bending angle between the two springs. Previous studies have theoretically shown that an unstable (stable) conformation based on the potential function can be stabilized (destabilized) by exciting spring vibration and stabilization or destabilization depends on amplitudes of vibration modes. However, the system was restricted in symmetric cases in which the two springs are identical and the masses of the two end beads are identical. This symmetry simplifies energy exchange between the vibration modes and conformation dynamics accordingly. We extend the theory into asymmetric systems. This extension can induce nontrivial energy exchange between the modes and a corresponding nontrivial conformation dynamics.

nlin.CD↗
arXiv2026

Inferring coupling strength and natural frequency distribution in coupled Stuart-Landau oscillators using linear response

We propose a framework to infer the coupling strength and the natural frequency distribution in a coupled Stuart-Landau oscillator system with a large population. The inference method uses observation of linear response of a macroscopic quantity and of an oscillator. We first solve the direct problem on the response with transforming the system into the phase-amplitude equations. Solving the inverse problem, we show that the coupling strength is inferred from observation of an oscillator and the natural frequency distribution from macroscopic responses. The proposed method requires only one-dimensional observation in the two-dimensional Stuart-Landau system. Validity of the inference theory is examined by numerical simulations.

nlin.AO↗
arXiv2026

Critical Scaling of Finite-Size Fluctuations around Marginal Stability in Long-Range Hamiltonian Systems

Finite size fluctuations are a crucial ingredient in kinetic theory of long-range interacting collisionless systems. In this Letter, we introduce a phenomenological theory which predicts an anomalous scaling close to marginal stability for these fluctuations. It also pinpoints the critical window inside which the fluctuations are anomalous, and outside which they are Gaussian. Shrinking very slowly as $N^{-1/5}$, this critical window encompasses a wide region around marginal stability. We confirm our predictions through extended numerical simulations on two different simplified models.

cond-mat.stat-mech↗
arXiv2025

Universality of discontinuous bifurcations in collisionless dynamics

We investigate the universality in collisionless nonlinear dynamics of a codimension-two bifurcation where two eigenvalues collide at the origin, and two lines of continuous bifurcation and discontinuous jump meet. Through linear analysis and direct numerical simulations, we show that this bifurcation does occur, both for two-dimensional shear flows and for repulsive systems mimicking plasmas.

nlin.PS↗
arXiv2024

Stabilization of a transition state by excited vibration and impact on the reaction rate in the three-body Lennard-Jones system

The three-body Lennard-Jones system on the plane has a transition state, which is the straight conformation located at a saddle point of the potential energy landscape. We show that the transition state can be dynamically stabilized by excited vibration of particle distances. The stabilization mechanism is explained theoretically, and is verified by performing molecular dynamics simulations. We also examine whether the dynamical stabilization gives an impact on the reaction rate between the two isomers of equilateral triangle conformations by comparing with the transition state theory.

nlin.CD↗
arXiv2022

Reconstruction of Phase Dynamics from Macroscopic Observations Based on Linear and Nonlinear Response Theories

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the responses with the system parameters including the time delay in interactions. We examine our method by applying it to two phase models, one of which describes a mean-field network of the Hodgkin--Huxley type neurons with a nonzero time delay. The method does not require much invasiveness nor microscopic observations, and these advantages highlight its broad applicability in various fields.

nlin.AO↗
arXiv2022

Discontinuous codimension-two bifurcation in a Vlasov equation

In a Vlasov equation, the destabilization of a homogeneous stationary state is typically described by a continuous bifurcation characterized by strong resonances between the unstable mode and the continuous spectrum. However, when the reference stationary state has a flat top, it is known that resonances drastically weaken, and the bifurcation becomes discontinuous. In this article, we use a combination of analytical tools and precise numerical simulations to demonstrate that this behavior is related to a codimension-two bifurcation, which we study in details.

nlin.PS↗
arXiv2022

Mode selectivity of dynamically induced conformation in many-body chain-like bead-spring model

We consider conformation of a chain consisting of beads connected by stiff springs, where the conformation is determined by the bending angles between the consecutive two springs. A conformation is stabilized or destabilized not only by a given bending potential but also the fast spring motion, and stabilization by the spring motion depends on their excited normal modes. This stabilization mechanism has been named the dynamically induced conformation in a previous work on a three-body system. We extend analyses of the dynamically induced conformation in many-body chain-like bead-spring systems. The normal modes of the springs depend on the conformation, and the simple rule of the dynamical stabilization is that the lowest eigenfrequency mode contributes to the stabilization of the conformation. The high the eigenfrequency is, the more the destabilization emerges. We verify theoretical predictions by performing numerical simulations.

nlin.CD↗
arXiv2022

Dynamically induced conformation depending on excited normal modes of fast oscillation

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential by using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified.

nlin.CD↗
arXiv2020

Critical exponents in coupled phase-oscillator models on small-world networks

A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is widely studied since it describes the synchronization transition, which emerges between the non-synchronized state and partially synchronized states. The synchronization transition is characterized by several critical exponents, and we focus on the critical exponent defined by coupling strength dependence of the order parameter for revealing universality classes. In a typical interaction represented by the perfect graph, an infinite number of universality classes is yielded by dependency on the natural frequency distribution and the coupling function. Since the synchronization transition is also observed in a model on a small-world network, whose number of links is proportional to the number of oscillators, a natural question is whether the infinite number of universality classes remains in small-world networks irrespective of the order of links. Our numerical results suggest that the number of universality class is reduced to one and the critical exponent is shared in the considered models having coupling functions up to the second harmonics with unimodal and symmetric natural frequency distributions.

nlin.AO↗
arXiv2020

Towards a classification of bifurcations in Vlasov equations

We propose a classification of bifurcations of Vlasov equations, based on the strength of the resonance between the unstable mode and the continuous spectrum on the imaginary axis. We then identify and characterize a new type of generic bifurcation where this resonance is weak, but the unstable mode couples with the Casimirs, which are constants of motion, to form a size 3 Jordan block. We derive a three-dimensional reduced noncanonical Hamiltonian system describing this bifurcation: coupling with the Casimirs controls the phase space portrait. Comparison of the reduced dynamics with direct numerical simulations on a test case gives excellent agreement. We finally discuss the relevance of this bifurcation to specific physical situations.

nlin.PS↗
arXiv2019

Classification of bifurcation diagrams in coupled phase-oscillator models with asymmetric natural frequency distributions

Synchronization among rhythmic elements is modeled by coupled phase-oscillators each of which has the so-called natural frequency. A symmetric natural frequency distribution induces a continuous or discontinuous synchronization transition from the nonsynchronized state, for instance. It has been numerically reported that asymmetry in the natural frequency distribution brings new types of bifurcation diagram having, in the order parameter, oscillation or a discontinuous jump which emerges from a partially synchronized state. We propose a theoretical classification method of five types of bifurcation diagrams including the new ones, paying attention to the generality of the theory. The oscillation and the jump from partially synchronized states are discussed respectively by the linear analysis around the nonsynchronized state and by extending the amplitude equation up to the third leading term. The theoretical classification is examined by comparing with numerically obtained one.

nlin.CD↗
arXiv2019

Critical exponents in mean-field classical spin systems

For a mean-field classical spin system exhibiting a second-order phase transition in the stationary state, we obtain within the corresponding phase space evolution according to the Vlasov equation the values of the critical exponents describing power-law behavior of response to a small external field. The exponent values so obtained significantly differ from the ones obtained on the basis of an analysis of the static phase-space distribution, with no reference to dynamics. This work serves as an illustration that cautions against relying on a static approach, with no reference to the dynamical evolution, to extract critical exponent values for mean-field systems.

cond-mat.stat-mech↗
arXiv2018

Collective $1/f$ fluctuation by pseudo-Casimir-invariants

In this study, we propose a universal scenario explaining the $1/f$ fluctuation, including pink noises, in Hamiltonian dynamical systems with many degrees of freedom under long-range interaction. In the thermodynamic limit, the dynamics of such systems can be described by the Vlasov equation, which has an infinite number of Casimir invariants. In a finite system, they become pseudoinvariants, which yield quasistationary states. The dynamics then exhibit slow motion over them, up to the timescale where the pseudo-Casimir-invariants are effective. Such long-time correlation leads to $1/f$ fluctuations of collective variables, as is confirmed by direct numerical simulations. The universality of this collective $1/f$ fluctuation is demonstrated by taking a variety of Hamiltonians and changing the range of interaction and number of particles.

nlin.CD↗
arXiv2018

A role of asymmetry in linear response of globally coupled oscillator systems

The linear response is studied in globally coupled oscillator systems including the Kuramoto model. We develop a linear response theory which can be applied to systems whose coupling functions are generic. Based on the theory, we examine the role of asymmetry introduced to the natural frequency distribution, the coupling function, or the coupling constants. A remarkable difference appears in coexistence of the divergence of susceptibility at the critical point and a nonzero phase gap between the order parameter and the applied external force. The coexistence is not allowed by the asymmetry in the natural frequency distribution but can be realized by the other two types of asymmetry. This theoretical prediction and the coupling-constant dependence of the susceptibility are numerically verified by performing simulations in $N$-body systems and in reduced systems obtained with the aid of the Ott-Antonsen ansatz.

nlin.AO↗
arXiv2017

Low-frequency discrete breathers in long-range systems without on-site potential

We propose a new mechanism of long-range coupling to excite low-frequency discrete breathers without the on-site potential. This mechanism is universal in long-range systems irrespective of the spatial boundary conditions, of topology of the inner degree of freedom, and of precise forms of the coupling functions. The limit of large population is theoretically discussed for the periodic boundary condition. Existence of discrete breathers is numerically demonstrated with stability analysis.

nlin.PS↗