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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.

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The critical value pc for correlated networks.In each panel, the numerically obtained values of the critical fraction pc are plotted against the assortativity coefficient r for random and targeted inactivation. The system size is N = 3000. The uncorrelated network with r ≈ 0 is given by the Erdős-Rényi random graph [40] in (a) and (b) and by the BA scale-free network [41] in (c) and (d). (a) Networks with Poisson degree distributions, generated by the GER method. (b) Networks with Poisson degree distributions, generated by the SER method. (c) Networks with power-law degree distributions, generated by the GER method. (d) Networks with power-law degree distributions, generated by the SER method.
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pone.0123722.g003: The critical value pc for correlated networks.In each panel, the numerically obtained values of the critical fraction pc are plotted against the assortativity coefficient r for random and targeted inactivation. The system size is N = 3000. The uncorrelated network with r ≈ 0 is given by the Erdős-Rényi random graph [40] in (a) and (b) and by the BA scale-free network [41] in (c) and (d). (a) Networks with Poisson degree distributions, generated by the GER method. (b) Networks with Poisson degree distributions, generated by the SER method. (c) Networks with power-law degree distributions, generated by the GER method. (d) Networks with power-law degree distributions, generated by the SER method.

Mentions: Figs 3(a) and 3(b) show the critical value pc for the networks generated by the GER and SER methods, respectively. For uncorrelated networks with r ≈ 0, the value of pc is the same for the three types of inactivation, because the way of oscillator inactivation is not significant in the homogeneously connected random network [6]. For the random inactivation in both panels, the value of pc is almost constant, independently of the r value. This is because the number of inactive oscillators in the neighborhood of each oscillator node is not affected by r. In fact, the oscillation amplitudes of the individual oscillators have similar distributions for disassortative, uncorrelated, and assortative networks (S1 and S2 Fig).


Robustness of oscillatory behavior in correlated networks.

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

The critical value pc for correlated networks.In each panel, the numerically obtained values of the critical fraction pc are plotted against the assortativity coefficient r for random and targeted inactivation. The system size is N = 3000. The uncorrelated network with r ≈ 0 is given by the Erdős-Rényi random graph [40] in (a) and (b) and by the BA scale-free network [41] in (c) and (d). (a) Networks with Poisson degree distributions, generated by the GER method. (b) Networks with Poisson degree distributions, generated by the SER method. (c) Networks with power-law degree distributions, generated by the GER method. (d) Networks with power-law degree distributions, generated by the SER method.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0123722.g003: The critical value pc for correlated networks.In each panel, the numerically obtained values of the critical fraction pc are plotted against the assortativity coefficient r for random and targeted inactivation. The system size is N = 3000. The uncorrelated network with r ≈ 0 is given by the Erdős-Rényi random graph [40] in (a) and (b) and by the BA scale-free network [41] in (c) and (d). (a) Networks with Poisson degree distributions, generated by the GER method. (b) Networks with Poisson degree distributions, generated by the SER method. (c) Networks with power-law degree distributions, generated by the GER method. (d) Networks with power-law degree distributions, generated by the SER method.
Mentions: Figs 3(a) and 3(b) show the critical value pc for the networks generated by the GER and SER methods, respectively. For uncorrelated networks with r ≈ 0, the value of pc is the same for the three types of inactivation, because the way of oscillator inactivation is not significant in the homogeneously connected random network [6]. For the random inactivation in both panels, the value of pc is almost constant, independently of the r value. This is because the number of inactive oscillators in the neighborhood of each oscillator node is not affected by r. In fact, the oscillation amplitudes of the individual oscillators have similar distributions for disassortative, uncorrelated, and assortative networks (S1 and S2 Fig).

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