Tipping induced by multiplexing on two-layer networks

We report the study of sudden transitions or tipping induced in a collection of systems due to multiplexing with another network of systems. The emergent dynamics of oscillators on one layer can undergo a sudden transition to steady state due to indirect coupling with a shared environment, mean field couplings and conjugate couplings among them. In all these cases, when multiplexed with another set of similar systems, the tipping phenomena are induced on the second layer also with a similar pattern of behavior. We consider van der Pol oscillator as nodal dynamics with various network topologies like scale-free and regular networks with local and nonlocal couplings. We also report how the coupling topology influences the nature of transitions on both layers, under multiplexing.