JPN/ENG

Hayato Chiba

Hayato Chiba

Professor (Mathematics)
Tohoku University,
Advanced Institute for Materials Research (AIMR),
Math Group,

2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

TEL: +81-22-217-6175
E-mail : hchiba (at) tohoku.ac.jp

Research Interest

I have been studying Dynamical Systems, especially singular perturbation theory, bifurcation theory, chaos, ODE on the complex plane, Painleve equaions. Most recently, I am interested in bifurcation theory in infinite dimensional spaces and its applications to synchronization phenomena in coupled ocsillators, machine learning, brain science, diabetes, etc.

In-phase synchronization of metronomes (the base is canned beers)

Anti-phase synchronization of metronomes (the base is PET bottles)

　

Coexisting two strange attractors of the Kuramoto model.

　

Papers

1. H.Chiba, "Weights, Kovalevskaya exponents and the Painleve property", Annales de l'Institut Fourier , in press, (2023). (pdf)

2. H.Chiba , M. Ikeda, I. Ishikawa, "Generalized eigenvalues of the Perron-Frobenius operators of symbolic dynamical systems", SIAM J. Appl. Dyn. Syst. , Vol.22, 2825-2855, (2023). (pdf)

3. H.Chiba, G.S. Medvedev, M.S. Mizuhara, " Bifurcations and patterns in the Kuramoto model with inertia", J. of Nonlinear Science ,(2023). (pdf)

4. H.Chiba, G.S. Medvedev, M.S. Mizuhara, "Instability of mixing in the Kuramoto model: From bifurcations to patterns", Pure and Applied Functional Analysis, Vol 7, Num 4, 1159-1172, (2022). (pdf)

5. H.Chiba, G. S. Medvedev, "Stability and bifurcation of mixing in the Kuramoto model with inertia", SIAM J. on Math. Analy. 54, pp. 1797-1819, (2022). (pdf),

6. H.Chiba, "Normal Forms of C^\infty Vector Fields based on the Renormalization Group", J. Math. Phys. , Vol.62, 062703, (2021) (pdf),

7. H.Chiba, "A Hopf bifurcation in the Kuramoto-Daido model", J. Diff. Equ. Vol.280, no 15, 546-570, (2021). (pdf).

8. K. Kotani, A. Akao, H.Chiba, "Bifurcation of the neuronal population dynamics of the modified theta model: transition to macroscopic gamma oscillation ", Physica D, Vol.416, 132789, (2021) . (pdf)

9. H.Chiba, G. S. Medvedev, "The mean field analysis of the Kuramoto model on graphs II. Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations", Discret. Contin. Dyn. S.-A, (2019), 39 (7), 3897-3921. (pdf)

10. H.Chiba, G. S. Medvedev, M. S. Muzuhara, "Bifurcations in the Kuramoto model on graphs", Chaos, 28, (2018), no.7, 073109, (pdf).

11. H.Chiba, G. S. Medvedev, "The mean field analysis for the Kuramoto model on graphs I. The mean field equation and transition point formulas", Discret. Contin. Dyn. S.-A, (2019), 39 (1), 131-155, (pdf).

12. H.Chiba, "A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions II : applications to Schrodinger operators", Kyushu Journal of Math. 72, 375-405 (2018), (pdf).

13. H.Chiba, "A center manifold reduction of the Kuramoto-Daido model with a phase-lag", SIAM j. on Appl. Dyn. Syst. Vol.16, No.3 (2017), (pdf).

14. H.Chiba, "Multi-Poisson approach to the Painleve equations: from the isospectral deformation to the isomonodromic deformation", SIGMA 13, 025 (2017), (pdf).

15. H.Chiba, "The third, fifth and sixth Painleve equations on weighted projective spaces",
    SIGMA 12, 019 (2016), (pdf).

16. H.Chiba, "Kovalevskaya exponents and the space of initial conditions of a quasi-homogeneous vector field",
    J. Diff. Equ. 259, no. 12, 7681-7716, (2015), (pdf).

17. H.Chiba, "The first, second and fourth Painleve equations on weighted projective spaces",
    J. Diff. Equ. 260, no. 2, 1263-1313, (2015), (pdf).

18. H.Chiba, "A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions",
    Adv. in Math. 273, 324-379, (2015), (pdf).

19. H.Chiba, "Reduction of weakly nonlinear parabolic partial differential equations",
    J. Math. Phys. 54, 101501, (2013), (pdf).

20. H.Chiba, "A proof of the Kuramoto conjecture for a bifurcation structure of the infinite dimensional Kuramoto model",
    Ergo. Theo. Dyn. Syst, 35, 762-834, (2015), (pdf)

21. H.Chiba, "Continuous limit of the moments system for the globally coupled phase oscillators",
    Discret. Contin. Dyn. S.-A, Vol.33, pp.1891-1903. (2013), (pdf)

22. H.Chiba, I.Nishikawa, "Center manifold reduction for a large population of globally coupled phase oscillators",
    Chaos, 21, 043103 (2011), (pdf)

23. H.Chiba, "Linear stability of the incoherent solution and the transition formula for the Kuramoto-Daido model",
    RIMS Kokyuroku Bessatsu, B21 (2010), (pdf)

24. H.Chiba, "Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points",
    J. Diff. Equ, 250, 112-160, (2011), (pdf)

25. M.Kuwamura, H.Chiba, "Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators",
    Chaos, 19, 043121 (2009), (pdf)

26. H.Chiba, "Extension and unification of singular perturbation methods for ODEs based on the renormalization group method",
    SIAM j. on Appl. Dyn.Syst., Vol.8, 1066-1115 (2009), (pdf)

27. H.Chiba, D.Pazo, "Stability of an [N/2]-dimensional invariant torus in the Kuramoto model at small coupling",
    Physica D, Vol.238, 1068-1081 (2009), (pdf)

28. H.Chiba, M.Iwasa, "Lie equations for asymptotic solutions of perturbation problems of ordinary differential equations",
    J. Math. Phys. 50 042703, (2009), (pdf)

29. H.Chiba, "Simplified renormalization group method for ordinary differential equations",
    J. Diff. Equ. 246, pp.1991-2019 , (2009), (pdf)

30. H.Chiba, "Approximation of center manifolds on the renormalization group method",
    J. Math. Phys. Vol.49, 102703 (2008), (pdf)

31. H.Chiba, "C^1 Approximation of vector fields based on the renormalization group method",
    SIAM j. on Appl. Dyn. Syst.,Vol.7, No.3, pp.895-932 (2008), (pdf)

Prepreint

H.Chiba, "The generalized spectral theory and its application to the Kuramoto conjecture ", (preprint).

H.Chiba, "A compactified Riccati equation of Airy type on a weighted projective space", (preprint).