Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn


Speaker: Hayato Chiba, Kyushu University, Japan

Title: A spectral theory of linear operators on a Gelfand triplet and its application to dynamics of coupled oscillators * Oberseminar Nichtlineare Dynamik

Time: Mon, Dec 15, 2014, 4:15pm

Place: bldg 28, room 2.100

The Kuramoto model is a system of ODEs (coupled oscillators) to describe synchronization phenomena. In this talk, an infinite dimensional Kuramoto model is considered, and Kuramoto's conjecture on a bifurcation diagram of the system will be proved.
A linear operator obtained from the linearization of the Kuramoto model has the continuous spectrum on the imaginary axis, so that the dynamics of the system cannot be revealed via the usual spectrum theory. To handle such continuous spectra, a new spectral theory of linear operators based on Gelfand triplets is developed. In particular, a generalized eigenvalue is defined. It is proved that a generalized eigenvalue determines the stability and bifurcation of solutions.

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Students' seminar: Theoretical Physics, PIK, Modeling & TSA Berlin-Potsdam-Colloquia: PhysGesellschaft Berlin, TU Berlin, Pro Physik, AIP, AEI, MPI-KGF, GFZ, HMI, PIK, AWI, Max Planck Institute for the History of Science, Mathematik, DPG Disputationen, & Vorschau UP

Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107
Phone: (+49-331) 977-1658, Fax : (+49-331) 977-1045

Email: Udo.Schwarz AT

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