In this paper we present an empirical study of the worldwide maritime transportation network (WMN) in which the nodes are ports and links are container liners connecting the ports. Using the different representation of network topology namely the space $L$ and $P$, we study the statistical properties of WMN including degree distribution, degree correlations, weight distribution, strength distribution, average shortest path length, line length distribution and centrality measures. We find that WMN is a small-world network with power law behavior. Important nodes are identified based on different centrality measures. Through analyzing weighted cluster coefficient and weighted average nearest neighbors degree, we reveal the hierarchy structure and "rich-club" phenomenon in the network.Comment: 10 pages, 11 figure

We study the vulnerability of complex networks under intentional attack with incomplete information, which means that one can only preferentially attack the most important nodes among a local region of a network. The known random failure and the intentional attack are two extreme cases of our study. Using the generating function method, we derive the exact value of the critical removal fraction fc of nodes for the disintegration of networks and the size of the giant component. To validate our model and method, we perform simulations of intentional attack with incomplete information in scale-free networks. We show that the attack information has an important effect on the vulnerability of scale-free networks. We also demonstrate that hiding a fraction of the nodes information is a cost-efficient strategy for enhancing the robustness of complex networks.

With the rapid development of metro systems in large Asian cities, such as Hong Kong and Shanghai, China, local authorities are developing park-and-ride (P&R) schemes to encourage commuters to reach the cities’ central areas by transferring from private cars to metro at stations with P&R facilities. A network equilibrium formulation can be used to model P&R services in a multimodal transportation network with elastic demand. It is assumed that commuters can complete their journeys by three options: auto mode, walk–metro mode, and P&R mode. The proposed model simultaneously considered commuters’ travel choices on travel mode, route–path, and transfer point, as well as their parking choice behavior. The effects of elastic travel demand, together with passengers’ discomfort in metro vehicles, were explicitly incorporated. The resultant problem can be formulated as an equivalent variational inequality problem. Numerical results showed that the introduction of P&R schemes could bring a positive, neutral, or even negative social welfare increment, and its efficiency depends greatly on the parking charging level and the number of parking spaces supplied at the P&R site and in the urban central area, as well as the metro dispatching frequency and fare.

We introduce a novel model for attack vulnerability of complex networks with a tunable attack information parameter. Based on the model, we study the attack vulnerability of complex networks based on local information. We employ the generating function formalism to derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component based on local information. We show that hiding just a small fraction of nodes can prevent the breakdown of a network and that it is a cost-efficient strategy for enhancing the robustness of complex networks to hide the information of networks.

A fractional order hyperchaotic system derived from a Liu system and its circuit realization *Han Qiang(韩 强) a)b) , Liu Chong-Xin(刘崇新) a)b) † , Sun Lei(孙 蕾) a)b) , and Zhu Da-Rui(朱大锐) a)b) a) State