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Many real-world networks interact with other networks by only several links, for example, transportation networks and aviation networks among cities, internet router network among the different regions, power supply network among cities and so on. Understanding how to protect these coupled networks and improve their robustness against cascading failures is very important. By protecting the edges between coupled networks, we investigate its efficiency on improving the robustness of coupled networks against cascading failures. Fixing the total protective cost of coupled networks, we find that adjusting the capacities of the edges among coupled networks can better improve the robustness of coupled networks against cascading failures and observe that the more uniform the distribution of the edge load, the more effective the protection strategy. In addition, by immunizing the edges among coupled networks, we compare two protecting methods and find that the immunization strategy can better protect coupled networks. Our results are useful not only for how to protect coupled networks from the local perspective, but also for significantly improving the robustness of a single network by protecting some key edges.

The development of modern economy makes the problem of traffic congestion increasingly serious. Many real traffic systems can be abstracted as that a variety of networks coupled and interconnected with each other. In this paper, the traffic dynamics on a double layer coupled network system is studied based on cellular automata model considering physical queuing. We explore the effect of maximal velocities in the two layer networks on the network capacity, and the mean and standard deviation of travel time. The results show that the increase of upper network velocity is beneficial to the traffic capacity and the efficiency of long-distance travel, but will also lead to larger deviation and lower reliability. We explain the phenomena by studying the usage of upper network. Finally, we investigate the vehicle distribution by adopting the Gini coefficient. It is found that the increase of upper network speed will make the traffic load distributed more uniformly in the system.

The study of traffic dynamics on couple networks is important for the design and management of many real systems. In this paper, an efficient routing strategy on coupled spatial networks is proposed, considering both traffic characteristics and network topology information. With the routing strategy, the traffic capacity can be greatly improved in both scenarios of identical and heterogeneous node capacity allocation. Heterogeneous allocation strategy of node delivery capacity performs better than identical capacity allocation strategy. The study can help to improve the performance of real-world multi-modal traffic systems.

The purpose of this work is to study coupled networks of nonidentical instances of the PCR system (Panic-Control-Reflex), which is a geographical model for human behaviors during catastrophic events. We endow the subsequent graph with superposed linear and quadratic couplings, and explore the effect of the topology of the network on the dynamics of each node. Especially, we investigate the possibility of controlling the panic level in the network by a clever disposal of the connections. We establish a necessary and sufficient condition for synchronization, without any reductive assumption on the nature of the network, and study the global stability of the trivial equilibrium. We illustrate our theoretical results by numerical simulations of randomly generated networks.

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in both networks. The model segregates the links in the networks as intra-links, cross-links and mix-links. The corresponding degree distributions of these links are found to be power-laws with exponents having coupled parameters for intra- and cross-links. In the weak coupling case, the model reduces to a simple citation network. As for the strong coupling, it mimics the mechanism of the web of human sexual contacts.

An extended model for coupled networks considering three possible links, i.e. rewiring links, direct links, and cross links, is proposed in this paper. Following the establishment of the master equations of degree distributions, the exact asymptotic solutions in power law form and their corresponding exponents are obtained. It is indicated that the minimal model used can describe the acquaintance webs well. The results also show that more other known consequences can be inferred just by tuning the parameters properly.