Description:

Takashi Nishikawa, Research Associate Professor, Department of Physics & Astronomy and Northwestern Institute on Complex Systems (NICO), Northwestern University

Synchronization -- An Insightful Example of Emergent Collective Dynamics on Complex Networks

Abstract
A fundamental question in studying complex systems concerns the dynamics-structure relation -- how do the characteristics of the interactions between dynamical units determine the dynamical behavior of the system? After more than a decade of research on the structure of real networks, the problem of understanding this relation has become a major topic of interest in network science. Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, serves as a great example of collective dynamical behavior of complex systems in which this relation can be systematically studied. In this talk, I will describe a powerful framework for conducting such a study, summarizing past and recent results on the dependence of synchronization stability on the network structure. Using synchronization as an example, I will present our results on a general phenomenon observed in network dynamics: the optimization of a collective dynamical property can give that property a sensitive, cusp-like dependence on network structural parameters. As an application to a genuine complex system of broad significance whose functioning depends critically on synchronization, I will discuss power-grid networks and our results on enhancing their stability.

Bio
Takashi Nishikawa, Research Associate Professor, Department of Physics & Astronomy and Northwestern Institute on Complex Systems (NICO), Northwestern University

Takashi Nishikawa is an interdisciplinary research scientist whose interests range from pure mathematics to realistic applications and intersect with diverse fields, including graph theory, dynamical systems, complex systems/networks, statistical physics, fluid dynamics, power system engineering, and systems biology. He focuses particularly on the relationship between the network structure and collective behavior in complex networks of coupled dynamical systems. He holds a Ph.D. in Applied Mathematics from University of Maryland, College Park, and his work has been published in Nature Physics, Proceedings of the National Academy of Sciences, and Physical Review Letters.