Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China.
Phys Rev E. 2018 Feb;97(2-1):022311. doi: 10.1103/PhysRevE.97.022311.
Synergistic interactions are ubiquitous in the real world. Recent studies have revealed that, for a single-layer network, synergy can enhance spreading and even induce an explosive contagion. There is at the present a growing interest in behavior spreading dynamics on multiplex networks. What is the role of synergistic interactions in behavior spreading in such networked systems? To address this question, we articulate a synergistic behavior spreading model on a double layer network, where the key manifestation of the synergistic interactions is that the adoption of one behavior by a node in one layer enhances its probability of adopting the behavior in the other layer. A general result is that synergistic interactions can greatly enhance the spreading of the behaviors in both layers. A remarkable phenomenon is that the interactions can alter the nature of the phase transition associated with behavior adoption or spreading dynamics. In particular, depending on the transmission rate of one behavior in a network layer, synergistic interactions can lead to a discontinuous (first-order) or a continuous (second-order) transition in the adoption scope of the other behavior with respect to its transmission rate. A surprising two-stage spreading process can arise: due to synergy, nodes having adopted one behavior in one layer adopt the other behavior in the other layer and then prompt the remaining nodes in this layer to quickly adopt the behavior. Analytically, we develop an edge-based compartmental theory and perform a bifurcation analysis to fully understand, in the weak synergistic interaction regime where the dynamical correlation between the network layers is negligible, the role of the interactions in promoting the social behavioral spreading dynamics in the whole system.
协同作用在现实世界中无处不在。最近的研究表明，对于单层网络，协同作用可以增强传播，甚至引发爆炸式的传播。目前，人们对多重网络上的行为传播动力学越来越感兴趣。在这种网络系统中，协同作用在行为传播中扮演什么角色？为了解决这个问题，我们在双层网络上构建了一个协同行为传播模型，其中协同作用的一个关键表现是节点在一层中采用一种行为会增强其在另一层中采用该行为的概率。一个普遍的结果是，协同作用可以大大增强两种行为在网络中的传播。一个显著的现象是，相互作用可以改变与行为采用或传播动力学相关的相变的性质。具体来说，取决于网络层中一种行为的传输率，协同作用可以导致另一种行为的采用范围相对于其传输率的不连续（一阶）或连续（二阶）相变。会出现一个令人惊讶的两阶段传播过程：由于协同作用，在一层中采用一种行为的节点会在另一层中采用另一种行为，然后促使该层中的其余节点快速采用这种行为。在分析中，我们开发了一种基于边缘的隔室理论，并进行了分支分析，以在弱协同作用的情况下（网络层之间的动态相关性可以忽略不计），充分理解相互作用在促进整个系统的社会行为传播动力学中的作用。
