Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:A4L-B

Session:

Number:239

Characterizing global dynamics on time-evolving networks of networks

Koji Iwayama,  Yoshito Hirata,  Hideyuki Suzuki,  Kazuyuki Aihara,  

pp.239-242

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.239

PDF download (710.8KB)

A network of networks, which consists of interconnected sub-networks, is ubiquitous in the real world. Methods for analyzing such networks have been proposed. Although these analyses focused on static structures of networks, most of real networks often change with time. Moreover, we often observe the dynamics on each node rather than the topology of the network. However, time-varying interactions among nodes have not been well characterized yet. Here, we propose a method to delineate time-evolving global topological structures on networks of networks. The proposed method roughly estimates the time-evolving structures, and characterizes the dynamics of their time-evolution using a distance.

[1] J. F. Donges, H. C. H. Schultz, N. Marwan, Y. Zou, and J. Kurths, “Investigating the topology of interesting networks-Theory and application to coupled climate subnetworks,” Eur. Phys. J. B, vol. 84, pp. 635-651, 2011.

[2] S. J. Schiff, P. So, T. Chang, R. E. Burke, and T. Sauer, “Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble,” Phys. Rev. E, vol. 54, pp. 6708-6724, 1996.

[3] J. Arnhold, P. Grassberger, K. Lehnertz, and C. E. Elger, “A robust method for detecting interdependences: application to intracranially recorded EEG,”Physica D, vol. 134, pp. 419-430, 1999.

[4] Y. Chen, G. Rangarajan, J. Feng, and M. Ding, “Analyzing multiple nonlinear time series with extended Granger causality,”Phys. Lett. A, vol. 324, pp. 26-35, 2004.

[5] D. Yu, M. Righero, and L. Kocarev, “Estimating topology of networks,”Phys. Rev. Lett., vol. 97, art. no. 188701, 2006.

[6] D. Napoletani and T. Sauer, “Reconstructing the topology of sparsely connected dynamical networks,”Phys. Rev. E, vol. 77, art. no. 026103, 2008.

[7] Y. Hirata and K. Aihara, “Identifying hidden common causes from bivariate time series: A method using recurrence plots,”Phys. Rev. E, vol. 81, art. no. 016203, 2010.

[8] K. Iwayama, Y. Hirata, K. Takahashi, K. Watanabe, K. Aihara, and H. Suzuki, “Characterizing global evolutions of complex systems via intermediate network representations,” Sci. Rep., vol. 2, art. no. 423, 2012.

[9] J. P. Eckmann, S. O. Kamphorst, and D. Ruelle, “Recurrence plots of dynamical Systems,”Europhys. Lett., vol. 4, pp. 973-977, 1987.

[10] N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence plots for the analysis of complex systems,” Phys. Rep., vol. 438, pp. 237-329, 2007.

[11] M. C. Romano, M. Thiel, J. Kurths, and W. von Bloh, “Multivariate recurrence plots,” Phys. Lett. A, vol. 330, pp. 214-223, 2004.

[12] M. Morris, M. S. Handcock, and D. R. Hunter, “Specification of exponential-family random graph models: terms and computational aspects,” J. Stat. Softw. vol. 24, pp. 1548-7660, 2008.