Explosive synchronization in populations of cooperative and competitive oscillators

Synchronization is a subject of interdisciplinary relevance, interpolating between efficiency in transportation and digital data transfers to disease in cardiac and neural tissue. While continuous transitions to synchronization are gradual and easy to control, explosive transitions may occur suddenly and can have catastrophic effects. Here we report that in populations of cooperative and competitive oscillators the transition can be tuned between continuous and explosive simply by adjusting the balance between the two oscillator types. We show that this phenomenon is independent of the network topology, and can be described analytically already in the mean-field approximation. Moreover, we provide evidence that the difference between the two transitions is due to a merging process of clusters which is forbidden by adaptation, and that the hysteresis associated to the explosive transition is enhanced when the adaptive mechanisms span larger scales.