On three oscillator universal probes for determining synchronization in arrays of coupled oscillators

Abstract

In a recent paper, Fink et al. described how a coupled array of three oscillators can serve as a universal probe of the synchronization properties in general coupled arrays of oscillators. However, the coupling topology in this probe is not optimal in experimental implementations. For instance, every oscillator is coupled to every other oscillator resulting in many coupling terms. Furthermore, the variable coupling weights at several coupling terms need to be set equal to each other. This means that some component values need to be varied over a range and be perfectly matched to each other in the experimental setup. We present simpler universal probes by utilizing the minimal number of coupling terms and by minimizing the constraint of having the coupling weights matched.