  We investigate the phenomenon of first order transition (explosive
synchronization (ES)) in adaptively coupled phase-frustrated bi-layer multiplex
network. We consider Sakaguchi-Kuramoto (SK) dynamics over the top of multiplex
networks and we establish that ES can emerge in all layers of a multiplex
network even when one of the layers may not exhibit ES in the absence of the
inter layer connections. We clearly identify the regions of the parameter
space, in which the multiplexity wins over frustration parameter and network
structure for the emergence of ES. Based on the mean field analysis around the
coherent state and a perturbative approach around the incoherent state we
analytically derive the synchronization transition points (backward and
forward) of all layers of multiplex network as well as its mono-layer
counterpart satisfying a close agreement with the numerical results.
