Dynamics of social contagions with memory of nonredundant information.
A key ingredient in social contagion dynamics is reinforcement, as adopting a certain social behavior requires verification of its credibility and legitimacy. Memory of nonredundant information plays an important role in reinforcement, which so far has eluded theoretical analysis. We first propose a general social contagion model with reinforcement derived from nonredundant information memory. Then, we develop a unified edge-based compartmental theory to analyze this model, and a remarkable agreement with numerics is obtained on some specific models. We use a spreading threshold model as a specific example to understand the memory effect, in which each individual adopts a social behavior only when the cumulative pieces of information that the individual received from his or her neighbors exceeds an adoption threshold. Through analysis and numerical simulations, we find that the memory characteristic markedly affects the dynamics as quantified by the final adoption size. Strikingly, we uncover a transition phenomenon in which the dependence of the final adoption size on some key parameters, such as the transmission probability, can change from being discontinuous to being continuous. The transition can be triggered by proper parameters and structural perturbations to the system, such as decreasing individuals' adoption threshold, increasing initial seed size, or enhancing the network heterogeneity.
Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
Wei
W
Wang
Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.|State key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Ming
M
Tang
School of Mathematical Science, Anhui University, Hefei 230039, China.
Hai-Feng
HF
Zhang
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Ying-Cheng
YC
Lai