Self-organizing synchronization with inhibitory-coupled oscillators

Solutions for time synchronization based on coupled oscillators operate in a self-organizing and adaptive manner and can be applied to various types of dynamic networks. The basic idea was inspired by swarms of fireflies, whose flashing dynamics shows an emergent behavior. This article introduces such a synchronization technique whose main components are “inhibitory coupling” and “self-adjustment.” Based on this new technique, a number of contributions are made. First, we prove that inhibitory coupling can lead to perfect synchrony independent of initial conditions for delay-free environments and homogeneous oscillators. Second, relaxing the assumptions to systems with delays and different phase rates, we prove that such systems synchronize up to a certain precision bound. We derive this bound assuming inhomogeneous delays and show by simulations that it gives a good estimate in strongly-coupled systems. Third, we show that inhibitory coupling with self-adjustment quickly leads to synchrony with a precision comparable to that of excitatory coupling. Fourth, we analyze the robustness against faulty members performing incorrect coupling. While the specific precision-loss encountered by such disturbances depends on system parameters, the system always regains synchrony for the investigated scenarios.