The Structural Robustness And Propagation Dynamics Of Interconnected Networks

With the development of society and technology, the phenomenon that a large number of small-scale networks gradually attached to large-scale networks and gradually formed larger interconnected networks emerged in the actual society. The difference in topology and dynamic behavior characteristics between interconnected network formed by interconnection behavior and the original large networks has attracted more and more attention. This paper proposed the interconnected network model on the basis of the interconnecting method( combining a dense small network to a large sparse network), and studied the structural robustness and dynamic behavior of the model. Which provided a guiding significance to analysis, control and use this interconnecting method.Structural robustness is an important reflection that weather a complex network can operate continuously and steadily after being destroyed, which is vital for network running. And has become the key for a system to survive under the condition of uncertainties and crisis. Using natural connectivity, algebraic connectivity and percolation analysis method, this paper has analyzed and studied the structural robustness of the proposed interconnected network model, and obtained three different conclusions: 1) The natural connectivity of the interconnected network is obviously increased compared to the large original network, which means that the interconnection behavior improved the structural robustness of network from the perspective of natural connectivity. 2) The algebraic connectivity of the interconnected network is significantly decreased compared to the original large network, which suggests that the structural robustness of network is reduced from the viewpoint of algebraic connectivity. 3) Percolation threshold and giant component of the interconnected network is similar to the original large network, which reflects that, in the case of random attack, the structural robustness of the network did not change visibly.Because of high spreading speed and great influence on society, epidemic spreading has always been a important research direction of dynamics on complex networks. Quantifying and controlling epidemic spreading and its cost has attracted more and more attention. Based on the Nonlinear Dynamics System Model(NLDS) and other mathematical tools(like matrix theory), we analyzed the epidemic threshold and cost of the interconnection network model. The results shows that: 1) Epidemic threshold of the interconnected network is obviously decreased compared to the large original network, which means that the epidemic in the interconnected network would be more easily erupt. 2) The total cost of the epidemic spreading over the entire interconnected network is almost unchanged compared to the large original network, which means that this interconnection behavior substantially reduce the epidemic threshold of the network, while the reduction of the epidemic threshold dose not change the overall epidemic costs.