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.