Since the work of Huygens in the 17th century, and continuing until the present day, there have been a steady stream of technological problems whose solution requires the synchronization of oscillators. In this talk we consider a general n-dimensional, autonomous differential equation model and investigate the types of coupling between the various modes that lead to synchronization. We will argue that when the coupling is weak there is a particular "simplest" form of coupling leading to synchronization and stability. The conclusions are based on a new result on eigenvalue placement and a complete analysis of the controllability of a class of systems with quadratic right-hand sides.
Welcome to everyone!