TY - JOUR
T1 - Explosive spreading on complex networks
T2 - The role of synergy
AU - Liu, Quan Hui
AU - Wang, Wei
AU - Tang, Ming
AU - Zhou, Tao
AU - Lai, Ying-Cheng
N1 - Funding Information:
This work was supported by the National Natural Science Foundation of China under Grants No. 11575041, No. 11105025, and No. 61433014, and the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2015J153). Y.C.L. was supported by ARO under Grant No. W911NF-14-1-0504.
PY - 2017/4/26
Y1 - 2017/4/26
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.95.042320
DO - 10.1103/PhysRevE.95.042320
M3 - Article
C2 - 28505757
AN - SCOPUS:85018352610
VL - 95
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 4
M1 - 042320
ER -