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

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)

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

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

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

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)

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)

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

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

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

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

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

H.Chiba, "A proof of the Kuramoto conjecture for a bifurcation structure of the infinite dimensional Kuramoto model", (pdf), Ergo. Theo. Dyn. Syst, (2013).

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

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 Jul/14/2014).

H.Chiba, "A spectral theory of linear operators on rigged Hilbert spaces under certain analyticity conditions", (preprint), (last modified Aug/20/2011)

H.Chiba, "A spectral theory of linear operators on rigged Hilbert spaces under certain analyticity conditions II : applications to Schrodinger operators", (preprint), (last modified Aug/21/2011)