Hybrid phase transitions driven by tug-of-war mechanism in complex dynamic systems

Hybrid phase transitions, exhibiting a jump of the order parameter and criticality at a transition point, are observed in diverse complex systems. Examples include k-core percolation, cascading breakdown in interdependent networks, contagion dynamics, restricted cluster coagulations, synchronization, etc. For such dynamical systems, it is a challenging task to uncover underlying mechanisms, and according to which the hybrid phase transitions are classified into universality classes. Here, we perform such tasks. Particularly, we focus on the case that the so-called tug-of-war mechanism between two temporal subgroups of the system induces hybrid phase transitions in dynamical systems such as percolation and synchronization. We show that in such dynamics, inter-event times between two successive crossings in the tug-of-war process have an inter-event time distribution that exhibits power-law decay behavior. The associated exponent determines the criticality of the hybrid percolation transition through cluster merging dynamics.