Wang Wei, Shu Panpan, Zhu Yu-Xiao, Tang Ming, Zhang Yi-Cheng
Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.
Department of Physics, University of Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland.
Chaos. 2015 Oct;25(10):103102. doi: 10.1063/1.4929761.
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.
个体总是受到一些缺乏弹性的资源的限制，比如时间和精力，这使得他们用于社交互动的时间有限，也限制了他们的接触能力。接触能力在社会传播动态中起着重要作用，而这一点迄今为止尚未得到理论分析。在本文中，我们首先提出一个非马尔可夫模型来理解接触能力对社会传播的影响，在该模型中，每个采用某种行为的个体只能与有限数量的邻居进行接触并传递信息。然后我们针对此模型发展了一种基于异质边的 compartmental 理论，并与模拟结果取得了显著的一致性。通过理论和模拟，我们发现扩大接触能力会使网络对于行为传播变得更加脆弱。有趣的是，我们发现最终采用规模对信息传播概率既可能存在连续依赖性，也可能存在非连续依赖性。这两种依赖性之间存在一种交叉现象。更具体地说，只有当度指数高于某个临界度指数时，扩大接触能力才会引发交叉现象，而当度指数低于临界度指数时，对于任何接触能力，最终行为采用规模总是持续增长。
