Explosive spreading on complex networks: The role of synergy

Quan Hui Liu, Wei Wang, Ming Tang, Tao Zhou, Ying-Cheng Lai

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


In spite of the vast literature on spreading dynamics on complex networks, the role of local synergy, i.e., the interaction of elements that when combined produce a total effect greater than the sum of the individual elements, has been studied but only for irreversible spreading dynamics. Reversible spreading dynamics are ubiquitous but their interplay with synergy has remained unknown. To fill this knowledge gap, we articulate a model to incorporate local synergistic effect into the classical susceptible-infected-susceptible process, in which the probability for a susceptible node to become infected through an infected neighbor is enhanced when the neighborhood of the latter contains a number of infected nodes. We derive master equations incorporating the synergistic effect, with predictions that agree well with the numerical results. A striking finding is that when a parameter characterizing the strength of the synergy reinforcement effect is above a critical value, the steady-state density of the infected nodes versus the basic transmission rate exhibits an explosively increasing behavior and a hysteresis loop emerges. In fact, increasing the synergy strength can promote the spreading and reduce the invasion and persistence thresholds of the hysteresis loop. A physical understanding of the synergy promoting explosive spreading and the associated hysteresis behavior can be obtained through a mean-field analysis.

Original languageEnglish (US)
Article number042320
JournalPhysical Review E
Issue number4
StatePublished - Apr 26 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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