Limits...
Robustness of oscillatory behavior in correlated networks.

Sasai T, Morino K, Tanaka G, Almendral JA, Aihara K - PLoS ONE (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

ABSTRACT
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.

Show MeSH

Related in: MedlinePlus

Adjacency matrices of scale-free networks.The dots located at (i, j) indicate the presence of the edges between node i and node j. (a) An uncorrelated network with r ≈ 0. (b) An assortative network with r = 0.4, generated by the GER method. (c) The same as (b), but generated by the SER method. (d) A disassortative network with r = −0.48, generated by the GER method. (e) The same as (d), but generated by the SER method.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4403822&req=5

pone.0123722.g004: Adjacency matrices of scale-free networks.The dots located at (i, j) indicate the presence of the edges between node i and node j. (a) An uncorrelated network with r ≈ 0. (b) An assortative network with r = 0.4, generated by the GER method. (c) The same as (b), but generated by the SER method. (d) A disassortative network with r = −0.48, generated by the GER method. (e) The same as (d), but generated by the SER method.

Mentions: The similarity and difference between the correlated scale-free networks generated by the two edge-rewiring methods are clarified in Fig 4. Fig 4(a) shows the adjacency matrix of the BA scale-free network with r ≈ 0 [41]. The dots are dense in the upper-right corner due to the hubs which have a large number of edges.


Robustness of oscillatory behavior in correlated networks.

Sasai T, Morino K, Tanaka G, Almendral JA, Aihara K - PLoS ONE (2015)

Adjacency matrices of scale-free networks.The dots located at (i, j) indicate the presence of the edges between node i and node j. (a) An uncorrelated network with r ≈ 0. (b) An assortative network with r = 0.4, generated by the GER method. (c) The same as (b), but generated by the SER method. (d) A disassortative network with r = −0.48, generated by the GER method. (e) The same as (d), but generated by the SER method.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4403822&req=5

pone.0123722.g004: Adjacency matrices of scale-free networks.The dots located at (i, j) indicate the presence of the edges between node i and node j. (a) An uncorrelated network with r ≈ 0. (b) An assortative network with r = 0.4, generated by the GER method. (c) The same as (b), but generated by the SER method. (d) A disassortative network with r = −0.48, generated by the GER method. (e) The same as (d), but generated by the SER method.
Mentions: The similarity and difference between the correlated scale-free networks generated by the two edge-rewiring methods are clarified in Fig 4. Fig 4(a) shows the adjacency matrix of the BA scale-free network with r ≈ 0 [41]. The dots are dense in the upper-right corner due to the hubs which have a large number of edges.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus