ABSTRACT: Recent progresses in functional magnetic resonance imaging techniques have demonstrated that human brains exhibit clustered correlation patterns of their spontaneous activities. It is important to understand the mechanism of cluster synchronization phenomena since it may reflect the underlying brain functions and brain diseases. In this talk, we discuss cluster synchronization conditions based on the model of Kuramoto oscillators’ networks. The key analytical tool that we use is the method of averaging, and we provide a unified framework of stability analysis for cluster synchronization. The main results show that cluster synchronization is achieved if (i) the inter-cluster coupling strengths are sufficiently weak and/or (ii) the natural frequencies are largely different among clusters. Moreover, we apply our theoretical findings to numerical simulations with empirical brain networks. We will also present other recent applications of oscillator networks from the view point of fault tolerance and cyber security.

BIOSKETCH: Hideaki Ishii received the M.Eng. degree from Kyoto University in 1998, and the Ph.D. degree from the University of Toronto in 2002. He was a Postdoctoral Research Associate at the University of Illinois at Urbana-Champaign from 2001 to 2004, and a Research Associate at The University of Tokyo from 2004 to 2007. Currently, he is a Professor in the Department of Computer Science, Tokyo Institute of Technology. He has held visiting positions at the University of Stuttgart, the Politecnico di Torino and CNR-IEIIT, Technical University of Berlin, and City University of Hong Kong. His research interests are in networked control systems, multi-agent systems, distributed algorithms, and cyber security of control systems.

Dr. Ishii has served as an Associate Editor for the IEEE Control Systems Letters, and Mathematics of Control, Signals, and Systems, and previously for Automatica, the IEEE Transactions on Automatic Control, and the IEEE Transactions on Control of Network Systems. He is the IPC Chair for the IFAC World Congress 2023 to be held in Yokohama, Japan. He serves as a Vice President for the IEEE Control Systems Society. He received the IEEE Control Systems Magazine Outstanding Paper Award in 2015. Dr. Ishii is an IEEE Fellow.