Hayato Chiba

Hayato Chiba

Department of Applied Mathematics and Physics,
Graduate School of Informatics,
Kyoto University, Kyoto 606-8501, Japan
E-mail : chiba at amp.i.kyoto-u.ac.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 have been investigating Renormalization Group Method, which is one of the most powerful singular perturbation methods. I am also interested in coupled ocsillators and synchronization.

　

For the brief review of the renormalization group method, see the pdf file below:

H. Chiba, "Renormalization Group Method and its Application to the Coupled Oscillators", (Japanese,English), (last modified Apr/08/2008)

　

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), (last modified Apr/21/2008)

H.Chiba, "Approximation of Center Manifolds on the Renormalization Group Method", J. Math. Phys. Vol.49, 102703 (2008) (pdf), (last modified Apr/27/2008)

H.Chiba, "Simplified Renormalization Group Method for Ordinary Differential Equations", J. Diff. Equ. 246, (2009), pp.1991-2019 (pdf), (last modified Sep/22/2008)

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

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), (last modified Mar/03/2008)

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), (last modified May/1/2009)

H.Chiba, "Fast-slow systems with Bogdanov-Takens type fold points", (preprint), (last modified Jul/10/2009)

H.Chiba, M.Kuwamura, "Bursting oscillations and chaos in a prey-predator system with dormancy of predators", (preprint),

H.Chiba, I.Aihara, N.Tsukamoto, "In-phase and anti-phase synchronization of coupled metronomes", (in preparation)

Schedule

Talks in Conferences and Workshops

Internatinal Conferences

"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)

Domestic Conferences

"Renormalization Group method and its application to coupled oscillators",Mathematical Analysis of pattern dynamics and related topics, Kyoto, Japan, (Jun, 2008)

"Renormalization Group method and its application to coupled oscillators",Nonlinear science related to biological phenomena, Kyoto, Japan, (Mar, 2008)

"Extension and Unification of Traditional Singular Perturbation Methods for ODEs",Annual meeting of Mathematical Society of Japan, Kinki-univ., Japan (Mar, 2008)

"Fast-Slow Systems with Codimension 2 Critical Manifolds", Dynamical systems workshop, Karuizawa, Japan (Jan,2008)

"Approximation of Vector Fields on the Renormalization Group Method and its application to the synchronization", Applications of RG Methods in Mathematical Sciences, Kyoto ,Japan (Sep, 2007)

"Higher Order Approxiamtion of Vector Fields on the Renormalization Group Method", New trends of dynamical systems and its applications, Kyoto, Japan, (Jun, 2007)

"C^1 Approximation of Vector Fields on the Renormalization Group Method", The 3rd COE Conference for Young Researchers, Hokkaido, Japan (Feb, 2007)

"C^1 Approximation of Vector Fields on the Renormalization Group Method and its Applications", dynamical systems workshop, Tokyo, Japan (Jan, 2007)