Unraveling the primary mechanisms leading to synchronization response in dissimilar oscillators

We study how the phenomenon of response to synchronization arises in sets of pulse-coupled dissimilar oscillators. One of the sets is constituted by oscillators that can easily synchronize. Conversely, the oscillators of the other set do not synchronize. When the elements of the first set are not synchronized, they induce oscillation death in the constituents of the second set. By contrast, when synchronization is achieved in oscillators of the first set, those of the second set recover their oscillatory behavior and thus, responding to synchronization. Additionally, we found another interesting phenomenon in this type of systems, namely, a new control of simultaneous firings in a population of similar oscillators attained by means of the action of a dissimilar oscillator.