Joint effect of ageing and multilayer structure prevents ordering in the voter model

The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in complex networks. Additionally, multilayer networks produce profound changes in the dynamics of models. In this work, we investigate how a multilayer structure affects the dynamics of an ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q*. Above it, the voter model always orders to an absorbing configuration. While, below, a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking in which the majority opinion in the different layers takes opposite signs and that due to the ageing indefinitely delay the arrival at the absorbing state.Comment: 10 pages, 8 figure

Clustered marginalization of minorities during social transitions induced by co-evolution of behaviour and network structure

Large-scale transitions in societies are associated with both individual behavioural change and restructuring of the social network. These two factors have often been considered independently, yet recent advances in social network research challenge this view. Here we show that common features of societal marginalization and clustering emerge naturally during transitions in a co-evolutionary adaptive network model. This is achieved by explicitly considering the interplay between individual interaction and a dynamic network structure in behavioural selection. We exemplify this mechanism by simulating how smoking behaviour and the network structure get reconfigured by changing social norms. Our results are consistent with empirical findings: The prevalence of smoking was reduced, remaining smokers were preferentially connected among each other and formed increasingly marginalised clusters. We propose that self-amplifying feedbacks between individual behaviour and dynamic restructuring of the network are main drivers of the transition. This generative mechanism for co-evolution of individual behaviour and social network structure may apply to a wide range of examples beyond smoking.Comment: 16 pages, 5 figure

Consensus dynamics on temporal hypergraphs

We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multiway interactions. We compare these consensus processes with dynamics evolving on projections that remove the temporal and/or the multiway interactions of the higher-order network representation. For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multiway interactions is slower than the convergence of the corresponding system with pairwise interactions, which in turn exhibits a slower convergence rate than a consensus dynamics on the corresponding static network. We then consider a nonlinear consensus dynamics model in the temporal setting. Here we find that in addition to an effect on the convergence speed, the final consensus value of the temporal system can differ strongly from the consensus on the aggregated, static hypergraph. In particular, we observe a first-mover advantage in the consensus formation process: If there is a local majority opinion in the hyperedges that are active early on, then the majority in these first-mover groups has a higher influence on the final consensus value-a behavior that is not observable in this form in projections of the temporal hypergraph

Collective Decision Dynamics in the Presence of External Drivers

We develop a sequence of models describing information transmission and decision dynamics for a network of individual agents subject to multiple sources of influence. Our general framework is set in the context of an impending natural disaster, where individuals, represented by nodes on the network, must decide whether or not to evacuate. Sources of influence include a one-to-many externally driven global broadcast as well as pairwise interactions, across links in the network, in which agents transmit either continuous opinions or binary actions. We consider both uniform and variable threshold rules on the individual opinion as baseline models for decision-making. Our results indicate that 1) social networks lead to clustering and cohesive action among individuals, 2) binary information introduces high temporal variability and stagnation, and 3) information transmission over the network can either facilitate or hinder action adoption, depending on the influence of the global broadcast relative to the social network. Our framework highlights the essential role of local interactions between agents in predicting collective behavior of the population as a whole.Comment: 14 pages, 7 figure