Topological synchronization of coupled nonlinear oscillators

Topological materials have attracted much interest due to their robust properties associated with gapless edge modes. On another front, synchronization of nonlinear oscillators can be found throughout nature, such as biological oscillators. Here, we combine these two fields of physics and reveal the topological way to control synchronization. Specifically, we find the topological synchronized state where the edge oscillators are synchronized while the bulk ones are chaotic. We conduct the Lyapunov analysis and numerically show that the Lyapunov vectors are localized at the edge of the system, which is analogous to edge modes in topological materials. We also propose the application of the topological synchronized state to on-demand pattern designing of synchronized oscillators, and thus the topological synchronization can be useful to robustly control the synchronization.