Many modern and important technological, social, information and infrastructure systems can be viewed as complex systems with a large number of interacting components. Models of complex networks and dynamical interactions, as well as their applications are of fundamental interests in many aspects. Here, several stylized models of multiplex propagation and opinion dynamics are investigated on complex and empirical social networks.

We first investigate cascade dynamics in threshold-controlled (multiplex) propagation on random geometric networks. We find that such local dynamics can serve as an efficient, robust, and reliable prototypical activation protocol in sensor networks in responding to various alarm scenarios. We also consider the same dynamics on a modified network by adding a few long-range communication links, resulting in a small-world network. We find that such construction can further enhance and optimize the speed of the network’s response, while keeping energy consumption at a manageable level.

We also investigate a prototypical agent-based model, the Naming Game, on two-dimensional random geometric networks. The Naming Game [A. Baronchelli et al., J. Stat. Mech.: Theory Exp. (2006) P06014.] is a minimal model, employing local communications that captures the emergence of shared communication schemes (languages) in a population of autonomous semiotic agents. Implementing the Naming Games with local broadcasts on random geometric graphs, serves as a model for agreement dynamics in large-scale, autonomously operating wireless sensor networks. Further, it captures essential features of the scaling properties of the agreement process for spatially-embedded autonomous agents. Among the relevant observables capturing the temporal properties of the agreement process, we investigate the cluster-size distribution and the distribution of the agreement times, both exhibiting dynamic scaling. We also present results for the case when a small density of long-range communication links are added on top of the random geometric graph, resulting in a “small-world”-like network and yielding a significantly reduced time to reach global agreement. We construct a finite-size scaling analysis for the agreement times in this case.

When applying the model of Naming Game on empirical social networks, this stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. We find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.