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The dynamics of cascading failures in spatial interdependent networkssignificantly depend on the interaction range of dependency couplings betweenlayers. In particular, for increasing range of dependency couplings, differenttypes of phase transition accompanied by various cascade kinetics can beobserved including mixed-order transition characterized by critical branchingphenomena, first-order transition with nucleation cascades, and continuoussecond-order transition with weak cascades. We also describe the dynamics ofcascades at the mutual mixed-order resistive transition in interdependentsuperconductors and show its similarity to that of percolation ofinterdependent abstract networks. Finally, we layout our perspectives for theexperimental observation of these phenomena, their phase diagrams and theunderlying kinetics, in the context of physical interdependent networks. Ourstudies of interdependent networks shed light on the possible mechanisms ofthree known types of phase transitions, second order, first order, and mixedorder as well as predicting a novel fourth type where a microscopicintervention will yield a macroscopic phase transition.

Dynamics of cascades in spatial interdependent networks