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Explosive synchronization refers to an abrupt (first order) transition tonon-zero phase order parameter in oscillatory networks, underpinned by thebistability of synchronous and asynchronous states. Growing evidence suggeststhat this phenomenon might be no less general then the celebrated Kuramotoscenario that belongs to the second order universality class. Importantly, therecent examples demonstrate that explosive synchronization can occur forcertain network topologies and coupling types, like the global higher-ordercoupling, without specific requirements on the individial oscillator dynamicsor dynamics-network correlations. Here we demonstrate a rich picture ofexplosive synchronization and desynchronization transitions in multiplexnetworks, where it is sufficient to have a single random sparsly connectedlayer with higher-order coupling terms (and not necessarily in thesynchronization regime on its own), the other layer being a regular latticewithout own phase transitions at all. Moreover, explosive synchronizationemerges even when the random layer has only low-order pairwise coupling,althoug the hysteresis interval becomes narrow and explosive desynchronizationis no longer observed. The relevance to the normal and pathological dynamics ofneural-glial networks is pointed out.

Explosive synchronization in multiplex neuron-glial networks