76 citations · 300 across the 26 of their papers we have counts for
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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…
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…
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…
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…
Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points
Hayato Chiba
The existence of stable periodic orbits and chaotic invariant sets of singularly perturbed problems of fast-slow type having Bogdanov-Takens bifurcation points in its fast subsyste…