title: Dynamics of social contagions with limited contact capacity.
abstract: Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacities. Contact capacity plays an important role in dynamics of social contagions, which so far has eluded theoretical analysis. In this paper, we first propose a non-Markovian model to understand the effects of contact capacity on social contagions, in which each adopted individual can only contact and transmit the information to a finite number of neighbors. We then develop a heterogeneous edge-based compartmental theory for this model, and a remarkable agreement with simulations is obtained. Through theory and simulations, we find that enlarging the contact capacity makes the network more fragile to behavior spreading. Interestingly, we find that both the continuous and discontinuous dependence of the final adoption size on the information transmission probability can arise. There is a crossover phenomenon between the two types of dependence. More specifically, the crossover phenomenon can be induced by enlarging the contact capacity only when the degree exponent is above a critical degree exponent, while the final behavior adoption size always grows continuously for any contact capacity when degree exponent is below the critical degree exponent.
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Wang
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Panpan
authors.initials: P
authors.lastname: Shu
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Yu-Xiao
authors.initials: YX
authors.lastname: Zhu
authors.affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
authors.forename: Ming
authors.initials: M
authors.lastname: Tang
authors.affiliation: Department of Physics, University of Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland.
authors.forename: Yi-Cheng
authors.initials: YC
authors.lastname: Zhang
mesh_terms: D003198:Computer Simulation; D006801:Humans; D033181:Information Dissemination; D008962:Models, Theoretical; D012944:Social Support