Summary
We discuss synchronization in networks of dynamical systems which interact via nonlinear coupling functions. First, we characterize nonlinear (potential) instabilities that drive systems apart in absence of coupling. Next, we constructively design nonlinear coupling functions that target these (potential) instabilities, therewith guaranteeing network synchronization. As the designed nonlinear coupling functions are active only when needed, these couplings are more energy efficient and less sensitive to output noise compared to linear coupling functions, which are commonly used to establish network synchronization. We demonstrate the performance advantages of our synchronizing nonlinear coupling by means of numerical simulations of a network with FitzHugh-Nagumo oscillators.
