Coupled adaptive complex networks

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuroscience and social sciences, as well as biology, engineering, and other disciplines. We show by theoretical analysis and computer simulations that multiplexing in a multilayer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Further, we develop a method for the analysis of Laplacian matrices of multiplex networks which allows for insight into the spectral structure of these networks enabling a reduction to the stability problem of single layers. We employ the multiplex decomposition to provide analytic results for the stability of the multilayer patterns. As local dynamics we use the paradigmatic Kuramoto phase oscillator, which is a simple generic model and has been successfully applied in the modeling of synchronization phenomena in a wide range of natural and technological systems.

The large graph limit of a stochastic epidemic model on a dynamic multilayer network

We consider a Markovian SIR-type (Susceptible → Infected → Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model where edges in different layers correspond to potentially infectious contacts of different types. We assume that the graph structure evolves in response to the epidemic via activation or deactivation of edges of infectious nodes. We derive a large graph limit theorem that gives a system of ordinary differential equations (ODEs) describing the evolution of quantities of interest, such as the proportions of infected and susceptible vertices, as the number of nodes tends to infinity. Analysis of the limiting system elucidates how the coupling of edge activation and deactivation to infection status affects disease dynamics, as illustrated by a two-layer network example with edge types corresponding to community and healthcare contacts. Our theorem extends some earlier results describing the deterministic limit of stochastic SIR processes on static, single-layer configuration model graphs. We also describe precisely the conditions for equivalence between our limiting ODEs and the systems obtained via pair approximation, which are widely used in the epidemiological and ecological literature to approximate disease dynamics on networks. The flexible modeling framework and asymptotic results have potential application to many disease settings including Ebola dynamics in West Africa, which was the original motivation for this study.

Competition of simple and complex adoption on interdependent networks

We consider the competition of two mechanisms for adoption processes: a so-called complex threshold dynamics and a simple susceptible-infected-susceptible (SIS) model. Separately, these mechanisms lead, respectively, to first-order and continuous transitions between nonadoption and adoption phases. We consider two interconnected layers. While all nodes on the first layer follow the complex adoption process, all nodes on the second layer follow the simple adoption process. Coupling between the two adoption processes occurs as a result of the inclusion of some additional interconnections between layers. We find that the transition points and also the nature of the transitions are modified in the coupled dynamics. In the complex adoption layer, the critical threshold required for extension of adoption increases with interlayer connectivity whereas in the case of an isolated single network it would decrease with average connectivity. In addition, the transition can become continuous depending on the detailed interlayer and intralayer connectivities. In the SIS layer, any interlayer connectivity leads to the extension of the adopter phase. Besides, a new transition appears as a sudden drop of the fraction of adopters in the SIS layer. The main numerical findings are described by a mean-field type analytical approach appropriately developed for the threshold-SIS coupled system.

Demand and Congestion in Multiplex Transportation Networks

Urban transportation systems are multimodal, sociotechnical systems; however, while their multimodal aspect has received extensive attention in recent literature on multiplex networks, their sociotechnical aspect has been largely neglected. We present the first study of an urban transportation system using multiplex network analysis and validated Origin-Destination travel demand, with Riyadh's planned metro as a case study. We develop methods for analyzing the impact of additional transportation layers on existing dynamics, and show that demand structure plays key quantitative and qualitative roles. There exist fundamental geometrical limits to the metro's impact on traffic dynamics, and the bulk of environmental accrue at metro speeds only slightly faster than those planned. We develop a simple model for informing the use of additional, "feeder" layers to maximize reductions in global congestion. Our techniques are computationally practical, easily extensible to arbitrary transportation layers with complex transfer logic, and implementable in open-source software.

Rescue of endemic states in interconnected networks with adaptive coupling

We study the Susceptible-Infected-Susceptible model of epidemic spreading on two layers of networks interconnected by adaptive links, which are rewired at random to avoid contacts between infected and susceptible nodes at the interlayer. We find that the rewiring reduces the effective connectivity for the transmission of the disease between layers, and may even totally decouple the networks. Weak endemic states, in which the epidemics spreads when the two layers are interconnected but not in each layer separately, show a transition from the endemic to the healthy phase when the rewiring overcomes a threshold value that depends on the infection rate, the strength of the coupling and the mean connectivity of the networks. In the strong endemic scenario, in which the epidemics is able to spread on each separate network –and therefore on the interconnected system– the prevalence in each layer decreases when increasing the rewiring, arriving to single network values only in the limit of infinitely fast rewiring. We also find that rewiring amplifies finite-size effects, preventing the disease transmission between finite networks, as there is a non zero probability that the epidemics stays confined in only one network during its lifetime.

Multiplex networks in metropolitan areas: generic features and local effects

Most large cities are spanned by more than one transportation system. These different modes of transport have usually been studied separately: it is however important to understand the impact on urban systems of coupling different modes and we report in this paper an empirical analysis of the coupling between the street network and the subway for the two large metropolitan areas of London and New York. We observe a similar behaviour for network quantities related to quickest paths suggesting the existence of generic mechanisms operating beyond the local peculiarities of the specific cities studied. An analysis of the betweenness centrality distribution shows that the introduction of underground networks operate as a decentralizing force creating congestion in places located at the end of underground lines. Also, we find that increasing the speed of subways is not always beneficial and may lead to unwanted uneven spatial distributions of accessibility. In fact, for London—but not for New York—there is an optimal subway speed in terms of global congestion. These results show that it is crucial to consider the full, multimodal, multilayer network aspects of transportation systems in order to understand the behaviour of cities and to avoid possible negative side-effects of urban planning decisions.

Absorbing and shattered fragmentation transitions in multilayer coevolution

We introduce a coevolution voter model in a multilayer by coupling a fraction of nodes across two network layers (the degree of multiplexing) and allowing each layer to evolve according to its own topological temporal scale. When these time scales are the same, the time evolution equations can be mapped to a coevolution voter model in a single layer with an effective average degree. Thus the dynamics preserve the absorbing-fragmentation transition at a critical value that increases with the degree of multiplexing. When the two layers have different topological time scales, we find an anomalous transition, named shattered fragmentation, in which the network in one layer splits into two large components in opposite states and a multiplicity of isolated nodes. We identify the growth of the number of components as a signature of this anomalous transition. We also find the critical level of interlayer coupling needed to prevent the fragmentation in a layer connected to a layer that does not fragment.