Search Results

Now showing 1 - 4 of 4
  • Item
    Robustness of interrelated traffic networks to cascading failures
    (London : Nature Publishing Group, 2014) Su, Z.; Li, L.; Peng, H.; Kurths, J.; Xiao, J.; Yang, Y.
    The vulnerability to real-life networks against small initial attacks has been one of outstanding challenges in the study of interrelated networks. We study cascading failures in two interrelated networks S and B composed from dependency chains and connectivity links respectively. This work proposes a realistic model for cascading failures based on the redistribution of traffic flow. We study the Barabási-Albert networks (BA) and Erd's-Rényi graphs (ER) with such structure, and found that the efficiency sharply decreases with increasing percentages of the dependency nodes for removing a node randomly. Furthermore, we study the robustness of interrelated traffic networks, especially the subway and bus network in Beijing. By analyzing different attacking strategies, we uncover that the efficiency of the city traffic system has a non-equilibrium phase transition at low capacity of the networks. This explains why the pressure of the traffic overload is relaxed by singly increasing the number of small buses during rush hours. We also found that the increment of some buses may release traffic jam caused by removing a node of the bus network randomly if the damage is limited. However, the efficiencies to transfer people flow will sharper increase when the capacity of the subway network αS > α0.
  • Item
    Low-dimensional behavior of Kuramoto model with inertia in complex networks
    (London : Nature Publishing Group, 2014) Ji, P.; Peron, T.K.D.M.; Rodrigues, F.A.; Kurths, J.
    Low-dimensional behavior of large systems of globally coupled oscillators has been intensively investigated since the introduction of the Ott-Antonsen ansatz. In this report, we generalize the Ott-Antonsen ansatz to second-order Kuramoto models in complex networks. With an additional inertia term, we find a low-dimensional behavior similar to the first-order Kuramoto model, derive a self-consistent equation and seek the time-dependent derivation of the order parameter. Numerical simulations are also conducted to verify our analytical results.
  • Item
    Synchronization in output-coupled temporal Boolean networks
    (London : Nature Publishing Group, 2014) Lu, J.; Zhong, J.; Tang, Y.; Huang, T.; Cao, J.; Kurths, J.
    This paper presents an analytical study of synchronization in an array of output-coupled temporal Boolean networks. A temporal Boolean network (TBN) is a logical dynamic system developed to model Boolean networks with regulatory delays. Both state delay and output delay are considered, and these two delays are assumed to be different. By referring to the algebraic representations of logical dynamics and using the semi-tensor product of matrices, the output-coupled TBNs are firstly converted into a discrete-time algebraic evolution system, and then the relationship between the states of coupled TBNs and the initial state sequence is obtained. Then, some necessary and sufficient conditions are derived for the synchronization of an array of TBNs with an arbitrary given initial state sequence. Two numerical examples including one epigenetic model are finally given to illustrate the obtained results.
  • Item
    Networks from Flows - From Dynamics to Topology
    (London : Nature Publishing Group, 2014) Molkenthin, N.; Rehfeld, K.; Marwan, N.; Kurths, J.
    Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.