Eemergent synchronous phenomena in complex systems are ubiquitous, e.g., cardiac pacemaker cells, biological clocks in brain and Josephson junction arrays and flashing of fireflies etc.
The Kuramoto model is the most well-known mathematical model for synchronization and has been extensively studied in the physics and engineering communities. Recently Max Lohe proposed a generalized matrix-valued ODE model extending the Kuramoto model as a special case. In this talk, we will discuss the formation and orbital stability of phase-locked states for the Kuramoto and Lohe models. This is a joint work with Sang Woo Ryoo.