Hayato Chiba

 

Hayato Chiba

Associate Professor
Institute of Mathematics for Industry,
Kyushu University,
744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

TEL: +81-92-802-4467
E-mail : chiba_at_imi_dot_kyushu-u_dot_ac_dot_jp


Research Interest

I have been studying Dynamical Systems, especially singular perturbation theory, bifurcation theory, and chaos. Most recently, I am interested in bifurcation theory in infinite dimensional spaces and its applications to coupled ocsillators.

In-phase synchronization of metronomes (with N.Tsukamoto, I.Aihara, mpg file, 8.42MB)

Anti-phase synchronization of metronomes (with N.Tsukamoto, I.Aihara, mpg file, 10.0MB)

 

Coexisting two strange attractors of the Kuramoto model.

 

Papers

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

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

  3. 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)

  4. 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)

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

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

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

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

  9. 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)

  10. 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)

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

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

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

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

H.Chiba, "The first, second and fourth Painleve equations on weighted projective spaces", (preprint). (last modified Jul/14/2014).

H.Chiba, "Kovalevskaya exponents and the space of initial conditions of a quasi-homogeneous vector field", (preprint). (last modified Aug/13/2015).

H.Chiba, "A spectral theory of linear operators on rigged Hilbert spaces under analyticity conditions II : applications to Schrodinger operators", (preprint), (last modified May/20/2015)

H.Chiba, "The third, fifth and sixth Painleve equations on weighted projective spaces", (preprint), (last modified Jun/1/2015)