Outer Synchronization between Two Coupled Complex Networks and Its Application in Public Traffic Supernetwork

Du, Wenju; Zhang, Jiangang; An, Xinlei; Qin, Shuang; Jiang, Yu

doi:10.1155/2016/8920764

Cited by 7 publications

(7 citation statements)

References 11 publications

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“…The network is responsible for handling 75% of road traffic, but it is inadequate, inferior, and unreliable. The highway network shows the characteristics of the small-world with various properties; Du et al (2016) [23] studied the synchronization problem of the urban bus hypernetwork model using the external synchronization theory of coupled complex network. Zhang et al (2018) [24] analyzed the network characteristics of three kinds of man and studied the vulnerability of man from two aspects of connectivity vulnerability and functional vulnerability by using two malicious attack methods; Ma et al (2020) [25] based on complex network theory, proposed a robust model of twolayer bus metro network from two aspects of structure and function.…”

Section: Research Of Hypernetwork In Trafficmentioning

confidence: 99%

“…The node degrees of 2836 bus stations in the bus hypernetwork and 88 metro stations in the metro hypernetwork are calculated respectively, and compared with the node degrees of 2924 nodes in the B-M hypernetwork, as shown in Figure 8. After the use of "Hyperedge" to connect the bus hypernetwork and the metro hypernetwork, the node degree of 2836 bus stations changed little, only 102 stations increased by 1, and the node degree value of other stations did not change; however, the change ratio of node degree of 88 metro stations was more extensive, and the difference was in the interval [23,72]. In the metro hypernetwork, the node degree of each station is related to the metro line.…”

Section: A Node Degreementioning

confidence: 99%

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Research on Bus and Metro Transfer From Perspective of Hypernetwork—A Case Study of Xi’an, China (December 2020)

Wang

Ren

2020

IEEE Access

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Aiming at the blank of hypernetwork in the empirical research field of the composite transportation network, taking Xi'an city as an example, this paper uses the "HyperEdge" to connect the bus network with the metro network and constructs a large-scale complex hypernetwork, hereinafter referred to as B-M hypernetwork. In this paper, the topological characteristics of a single hypernetwork are analogized to a complex hypernetwork, and the interaction mechanism among bus networks, metro networks, and B-M hypernetwork is studied. A multi-source least transferred algorithm based on the incidence matrix is proposed to solve any two nodes' minimum transfer times in a large complex hypernetwork. The multi-source least transferred algorithm and matrix transfer algorithm is applied to the B-M hypernetwork, and the random attack and intentional attack analyze the robustness of the B-M hypernetwork. The results show that the improved multi-source minimum transmission algorithm based on the incidence matrix is feasible and effective and can obtain superior computing power for large and complex hypernetworks.

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Section: Research Of Hypernetwork In Trafficmentioning

confidence: 99%

Section: A Node Degreementioning

confidence: 99%

Research on Bus and Metro Transfer From Perspective of Hypernetwork—A Case Study of Xi’an, China (December 2020)

Wang

Ren

2020

IEEE Access

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“…Choosing ξ(t) = e k (t − τ k (t)) or ξ(t) = e h (t) in (6) and substituting them into inequality (5) produces the following inequality chain, 5. An application to delayed coupled oscillators on NWSC.…”

Section: 2mentioning

confidence: 99%

“…Another kind of synchronization called outer synchronization was thus put forward in [16] to account for the phenomena that different CSNs could achieve synchronization regardless of synchronization of the inner nodes. Shortly after, outer synchronization has become a new and important topic in the research of CSNs and some results related to this issue have been obtained in [4,6,30].…”

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confidence: 99%

Outer synchronization of delayed coupled systems on networks without strong connectedness: A hierarchical method

Liu¹,

Li²

2018

Discrete &Amp; Continuous Dynamical Systems - B

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We consider the outer synchronization between drive-response systems on networks with time-varying delays, where we focus on the case when the underlying networks are not strongly connected. A hierarchical method is proposed to characterize large-scale networks without strong connectedness. The hierarchical algorithm can be implemented by some programs to overcome the difficulty resulting from the scale of networks. This method allows us to obtain two different kinds of sufficient outer synchronization criteria without the assumption of being strongly connected, by combining the theory of asymptotically autonomous systems with Lyapunov method and Kirchhoff's Matrix Tree Theorem in graph theory. The theory improves some existing results obtained by graph theory. As illustrations, the theoretic results are applied to delayed coupled oscillators and a numerical example is also given. 837 838 SHUANG LIU AND WENXUE LI OUTER SYNCHRONIZATION OF NETWORKS 839• We first analyze the OES between delayed coupled systems on NWSC by means of graph theory especially removing the assumption of a strongly connected network. The proposed theory presents generality and improves the existing results in above literatures.

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“…Du W J puts forward a supernetwork model of urban public transport composed of conventional public transport network and urban rail transit network. Based on the external synchronization theory of coupled complex networks, the synchronization problem of urban public transport supernetwork model is studied [23]. Suo Q takes station representation as node and line representation as superedge.…”

Section: Introductionmentioning

confidence: 99%

Establishment and Analysis of the Supernetwork Model for Nanjing Metro Transportation System

Wei

Sun

2018

Complexity

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In recent years, many researchers have applied complex network theory to urban public transport network to construct complex network and analyze its network performance. The original analysis method generally uses the Space L and Space R model to establish a simple link between public sites but ignores the organic link between the overall network system and the line subsystem. As an important part of urban public transport system, subway plays an important role in alleviating traffic pressure. In this paper, a supernetwork model of Nanjing metro network is established by using the supernetwork method. Three parameters, node-hyperedge degree, hyperedge-node degree, and hyperedge degree, are proposed to describe the model. The model is compared with the traditional Space L and Space P models. The study on the supernetwork model of Nanjing metro complex network shows that the network density, network centrality, and network clustering coefficient are large, and the average network distance is small, which meets the requirements of traffic planning and design. In this study, the subway line is considered as a subsystem and further simplified as a node, so that the complex network analysis method can be applied to the new supernetwork model, expanding the thinking of complex network research.

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Outer Synchronization between Two Coupled Complex Networks and Its Application in Public Traffic Supernetwork

Cited by 7 publications

References 11 publications

Research on Bus and Metro Transfer From Perspective of Hypernetwork—A Case Study of Xi’an, China (December 2020)

Research on Bus and Metro Transfer From Perspective of Hypernetwork—A Case Study of Xi’an, China (December 2020)

Outer synchronization of delayed coupled systems on networks without strong connectedness: A hierarchical method

Establishment and Analysis of the Supernetwork Model for Nanjing Metro Transportation System

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