Hayato Chiba

　

Hayato Chiba

Faculty of Mathematics,
Kyushu University,
744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

TEL: +81-92-802-4430
E-mail : chiba_at_imi_dot_kyushu-u_dot_ac_dot_jp
private web page (Japanese) : http://www18.ocn.ne.jp/~hchiba/

　


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", (preprint), (last modified Mar/26/2010)

H.Chiba, "A proof of the Kuramoto's conjecture for a bifurcation structure of the infinite dimensional Kuramoto model", (preprint), (last modified Jul/31/2010)

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)

　

Talks in Conferences and Workshops

Internatinal Conferences

"Bifurcation theory of the infinite-dimensional Kuramoto model", Universality and Scaling Limits in Probability and Statistical Mechanics, Hokkaido, Japan, (Aug, 2010)

"Bifurcation theory of the infinite-dimensional Kuramoto model", Symmetry Plus Integrability 2010, South Padre Island, Texas, (Jun, 2010)

"Extension and Unification of Traditional Singular Perturbation Methods for ODEs", SIAM Conference on Applications of Dynamical Systems, Snowbird, USA, (May, 2009)

"Extension and Unification of Traditional Singular Perturbation Methods for ODEs",Chinese Academy of Sciences - Kyoto University Joint Workshop on Mathematical Methods for Informatics, Engineering and Management, Beijing, China, (Mar, 2008)

"Approximation of Vector Fields on the Renormalization Group Method", SIAM Conference on Applications of Dynamical Systems, Snowbird, USA, (May, 2007)