第68回「非線形・統計力学とその周辺」セミナーのご案内

日時：平成１７年９月１３日（火）午後２時４５分〜午後３時４５分

場所：京都大学工学部総合校舎１０２室

講演者： Prof. J. Kurths (Potsdam Univ., Center for Dynamics of Complex Systems)

講演題目： Complex Synchronization: from Coupled Systems to Complex Networks

講演要旨：

Synchronization phenomena are abundant in nature, science,
engineering and social life. Synchronization was first recognized
by Christiaan Huygens in 1665 for coupled pendulum clocks; this was
the beginning of nonlinear sciences. First, several examples of
synchronization in periodic systems are presented, such as in
clocks, organ pipes, fireflies and even in the mechanics of bridges.
Second synchronization phenomena in coupled complex systems are
discussed. Then it is explained how to identify such phenomena
in experimental data and especially in physiological measurements,
such as MEG, EEG or heart rate data. Third I present two approaches
to detect and quantify phase synchronization in coupled non-phase
coherent oscillators. The first is based on the general idea of
curvature and the second one on the concept of recurrence. It is
shown that the second method is applicable even to noisy data.
Applications to electrochemical experiments are given.

Then synchronization in networks with complex topology are discussed.
Heterogeneity in the degree (connectivity) distribution has been
shown to suppress synchronization in networks of symmetrically
coupled oscillators with uniform coupling strength. In this talk
I present a condition which uncovers enhanced synchronization in
weighted networks with asymmetric coupling. It is shown that in
the optimum regime synchronizability is solely determined by the
average degree and does not depend on the system size and the
details of the degree distribution. In scale-free networks, where
the average degree may increase with heterogeneity, while the
overall cost involved in the network coupling is significantly
reduced as compared to the case of unweighted coupling.
Consequences for metabolic networks will be discussed.

Acknowledgements

This work was supported by the Humboldt foundation, SFB 555 (DFG),
INTAS and the financial support for a visiting professorship in
Cognitive Science at Potsdam University.

References

1.M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 1996, 76, 1804.
2.A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization ? A Universal Concept in Nonlinear Sciences, Cambridge University Press 2001.
3.S. Boccaletti, J. Kurths, G. Osipov, D. Valladares, and C. Zhou,  Phys. Rep. 2002, 366, 1.
4.G. Osipov, B. Hu, C. Zhou, and J. Kurths, Phys. Rev. Lett. 2003,  91, 024101.
5.M. Ivanchenko, G. Osipov, V. Shalfeev, and J. Kurths, Phys. Rev. Lett. 2004, 92, 134101.
6.M. Romano, M. Thiel, J. Kurths, and W. von Bloh, Phys. Lett. A 2004,  330, 214.
7.M. Romano, M. Thiel, J. Kurths, I. Kiss, and J. Hudson, Europhys.  Lett. 2005, 71, 466-472.
8.F. Meinecke, A. Ziehe, J. Kurths, and K. Muller, Phys. Rev. Lett.  2005, 94, 084102.
9.A. Motter, C. Zhou, and J. Kurths, Europhys. Lett. 2005, 69, 334.
10.A. Motter, C. Zhou, and J. Kurths, Phys. Rev. E 2005, 71, 016116.