Explosive synchronization in multiplex multiple timescale networks with higher-order interactions

Explosive synchronization refers to an abrupt (first order) transition to non-zero value of phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this phenomenon might be no less general then the celebrated Kuramoto scenario that belongs to the second order universality class. Importantly, the recent examples demonstrate that explosive synchronization can occur for global higher-order coupling without specific requirements on the individual oscillator dynamics or dynamics-network correlations. Here we demonstrate a rich picture of explosive (de)synchronization transition in multiplex networks, where it is sufficient to have a single random sparsely connected layer with higher-order coupling terms (and not necessarily in the synchronization regime on its own) and the other layer being a regular lattice without own phase transitions at all. Characteristic timescales in the layers have to be different. Moreover, explosive synchronization emerges even when the random layer has only low-order pairwise coupling, although the hysteresis interval becomes narrow and explosive desynchronization is no longer observed. The explosive transition persists with increasing the system size. The relevance to the normal and pathological dynamics of neural-glial networks is pointed out.