Practical and Theoretical Questions in Network Synchronization: Optimization and Control
Collective behavior in large ensembles of network-coupled dynamical systems remains an active area of research in the nonlinear dynamics and networks science communities. Example applications stem from both naturally-occurring to man-made systems, e.g., cardiac pacemaker cells, mammalian circadian rhythms, Josephson junctions, and power grids. Researchers’ efforts have illuminated rich nonlinear phenomena in heterogeneous oscillator systems, including the onset of synchronization, effects of community structure, and effects of time delay. However, important practical questions remain, including: (i) How can heterogeneous oscillator networks be optimized for synchronization? and (ii) What is the most efficient protocol for controlling heterogeneous oscillator networks? In this talk I will present a body of work that explores and answers these important questions. Central to this work is the development of the Synchrony Alignment Function, a theoretical tool and objective measure of collective behavior that quantifies the interplay between a complex network structure and the heterogeneous internal dynamics of each oscillator. Using this and other theoretical developments we implement solutions to practically constrained problems and explore the important structural and dynamical properties underlying to optimization and control of network synchronization.