76 citations · 300 across the 26 of their papers we have counts for
26 papers
Bifurcations and patterns in the Kuramoto model with inertia
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampl…
Generalized eigenvalues of the Perron-Frobenius operators of symbolic dynamical systems
Hayato Chiba, Masahiro Ikeda, Isao Ishikawa
The generalized spectral theory is an effective approach to analyze a linear operator on a Hilbert space with a continuous spectrum. The generalized spectrum is compu…
Stability and bifurcation of mixing in the Kuramoto model with inertia
Hayato Chiba, Georgi S. Medvedev
The Kuramoto model of coupled second order damped oscillators on convergent sequences of graphs is analyzed in this work. The oscillators in this model have random intrinsic freque…
Bifurcation of the neuronal population dynamics of the modified theta model: transition to macroscopic gamma oscillation
Kiyoshi Kotani, Akihiko Akao, Hayato Chiba
Interactions of inhibitory neurons produce gamma oscillations (30--80 Hz) in the local field potential, which is known to be involved in functions such as cognition and attention.…
Weights, Kovalevskaya exponents and the Painlevé property
Hayato Chiba
Weighted degrees of quasihomogeneous Hamiltonian functions of the Painlevé equations are investigated. A tuple of positive integers, called a regular weight, satisfying certain con…
Normal Forms of Vector Fields based on the Renormalization Group
Hayato Chiba
The normal form theory for polynomial vector fields is extended to those for vector fields vanishing at the origin. Explicit formulas for the normal form and…
Instability of mixing in the Kuramoto model: From bifurcations to patterns
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which c…
Bifurcations in the Kuramoto model on graphs
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifica…
The mean field analysis of the Kuramoto model on graphs II. Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations
Hayato Chiba, Georgi S. Medvedev
In our previous work [Chiba, Medvedev, arXiv:1612.06493], we initiated a mathematical investigation of the onset of synchronization in the Kuramoto model (KM) of coupled phase osci…
The mean field analysis for the Kuramoto model on graphs I. The mean field equation and transition point formulas
Hayato Chiba, Georgi S. Medvedev
In his classical work on synchronization, Kuramoto derived the formula for the critical value of the coupling strength corresponding to the transition to synchrony in large ensembl…
A Hopf bifurcation in the Kuramoto-Daido model
Hayato Chiba
A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency distribut…
A center manifold reduction of the Kuramoto-Daido model with a phase-lag
Hayato Chiba
A bifurcation from the incoherent state to the partially synchronized state of the Kuramoto-Daido model with the coupling function is investi…
Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation
Hayato Chiba
A multi-Poisson structure on a Lie algebra provides a systematic way to construct completely integrable Hamiltonian systems on expressed in Lax form $…
The Third, Fifth and Sixth Painlevé Equations on Weighted Projective Spaces
Hayato Chiba
The third, fifth and sixth Painlevé equations are studied by means of the weighted projective spaces with suitable weights determined by the N…
A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions II: applications to Schrödinger operators
Hayato Chiba
A spectral theory of linear operators on a rigged Hilbert space is applied to Schrödinger operators with exponentially decaying potentials and dilation analytic potentials. The the…
Kovalevskaya exponents and the space of initial conditions of a quasi-homogeneous vector field
Hayato Chiba
Formal series solutions and the Kovalevskaya exponents of a quasi-homogeneous polynomial system of differential equations are studied by means of a weighted projective space and dy…
The first, second and fourth Painlevé equations on weighted projective spaces
Hayato Chiba
The first, second and fourth Painlevé equations are studied by means of dynamical systems theory and three dimensional weighted projective spaces $\C P^3(p,q,r,s)$ with suitable we…
Reduction of weakly nonlinear parabolic partial differential equations
Hayato Chiba
It is known that the Swift-Hohenberg equation can be reduced to the Ginzburg-Landau equation (amplitude equat…
A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions
Hayato Chiba
A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator on a Hilbert space is…
Center manifold reduction for large populations of globally coupled phase oscillators
Hayato Chiba, Isao Nishikawa
A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensiona…
A proof of the Kuramoto conjecture for a bifurcation structure of the infinite dimensional Kuramoto model
Hayato Chiba
The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as a coupled phase oscillators. In this paper, a bifurcation stru…
Continuous limit of the moments system for the globally coupled phase oscillators
Hayato Chiba
The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on -torus defined as coupled harmonic oscillators. The order parame…
Linear stability of the incoherent solution and the transition formula for the Kuramoto-Daido model
Hayato Chiba
The Kuramoto-Daido model, which describes synchronization phenomena, is a system of ordinary differential equations on -torus defined as coupled harmonic oscillators, whose natu…
Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method
Hayato Chiba
The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this ar…