Feedback-induced critical behavior in binary propagation on complex networks

Abstract

While the phase transitions in binary propagation on complex networks have been studied a great deal from diverse fields during the past years, the effect of feedback has rarely been systematically addressed in a general manner. Here, we study a minimal network model of binary propagation with a general feedback effect. It is found that when the basic propagation rate is small, moderate positive feedback can induce bistable dynamics, resulting in an abrupt and discontinuous phase transition, which is absent in the case of negative feedback or no feedback. Moreover, the degree heterogeneity of the network further induces a hysteresis loop structure in this phase transition. It is also found that positive feedback accelerates spread before reaching the peak activity, whereas negative feedback has a contrary effect, which may uncover the origin of the accelerating spread observed in sophisticated models [S. V. Scarpino, A. Allard, and L. H\'ebert-Dufresne, Nat. Phys. 12, 1042 (2016)]. These findings reveal the universal and nontrivial effects of feedback on binary propagation dynamics. It can help to preestimate the phase-transition behavior in specific network propagation models and help to better understand the criticality of other dynamical processes on complex networks arising from different scientific backgrounds.