Robustness of oscillatory behavior in correlated networks.
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The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear.Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity.Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.
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Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
ABSTRACT
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Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity. Related in: MedlinePlus |
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Mentions: In the GER method, the edge rewiring is conducted based on the degrees of the connected node pairs. We sort the remaining degrees j1, j2, k1, and k2 in descending order and relabel them to l1, l2, l3 and l4 so that l1 ≥ l2 ≥ l3 ≥ l4. Fig 2(a) illustrates the three possibilities for separating the four nodes into two pairs of connected nodes. When increasing the assortativity coefficient, Case I is chosen to set the edges between the nodes with more similar degrees if the current state is Case II or III. When decreasing the assortativity coefficient, Case III is chosen to set an edge between the nodes with the largest and smallest degrees if the current state is Case I or II. We increase or decrease the assortativity coefficient by repeating the edge rewiring in a greedy way and continue until the assortativity coefficient is no longer changed. The assortativity coefficient r monotonically increases or decreases with this method. |
View Article: PubMed Central - PubMed
Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.