This paper introduces a synchronization technique inspired by the fascinating natural phenomenon of spontaneous synchronization. The authors cover a wide range of observed things that sync up spontaneously, ranging from male Asian fireflies with synchronous light flashes, to the 10,000 pacemaker cells that trigger the rest of the human heart to beat correctly. It is generally accepted that these occurrences of spontaneous synchronization arise from a completely distributed mechanism that is based on simple interactions between things.

The case of the Asian fireflies is modeled by a system of pulse-coupled oscillators. The oscillators interact by emitting and receiving pulse signals. An oscillator emits a pulse signal at the end of its phase. Upon reception of a pulse signal, another oscillator adjusts its own phase. A system of oscillators that obeys these simple rules eventually reaches a synchronized pulse signal emission. This solution can be applied to various types of dynamic networks.

Almost all approaches for the coupled oscillators model assume that the oscillator performs a positive phase jump (excitatory coupling). This paper considers a model that performs negative phase jumps (inhibitory coupling). The authors show that inhibitory coupling can lead to perfect synchrony independent of initial conditions for delay-free environments and homogeneous oscillators. They also show that inhibitory coupling with self-adjustment quickly leads to synchrony with a precision comparable to that of excitatory coupling. Their research shows that systems synchronize up to a certain precision bound, when the assumptions on delays and different phase rates are relaxed. Assuming inhomogeneous delays, they derive the bound and show via simulations that it gives a good estimate in strongly coupled systems. For the investigated scenarios, they analyze the robustness against faulty members performing incorrect coupling (Byzantine behavior) and find that the system always regains synchrony. The specific loss of precision encountered by such disturbances depends on system parameters.

This well-written paper investigates a spontaneous synchronization scheme with inhibitory coupling and self-adjustment. Understanding spontaneous order holds great promise for automation possibilities in large complex systems like computing clouds.