Recurrence Networks: Evolution and Robustness

We analyze networks generated by the recurrence plots of the time series of chaotic systems and study their properties, evolution and robustness against several types of attacks. Evolving recurrenc...

[1]  Jin Zhou,et al.  Scale-free networks which are highly assortative but not small world. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Zhongke Gao,et al.  Complex network from time series based on phase space reconstruction. , 2009, Chaos.

[3]  Bethany S. Dohleman Exploratory social network analysis with Pajek , 2006 .

[4]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[5]  Michael Small,et al.  Transforming Time Series into Complex Networks , 2009, Complex.

[6]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[7]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[8]  L. Tjeng,et al.  Orbitally driven spin-singlet dimerization in S=1 La4Ru2O10. , 2006, Physical review letters.

[9]  L. Wahl,et al.  Perspectives on the basic reproductive ratio , 2005, Journal of The Royal Society Interface.

[10]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[11]  V. Liu,et al.  On the initial expansion of meteor trails , 1976 .

[12]  Zhongke Gao,et al.  Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Michael Small,et al.  Superfamily phenomena and motifs of networks induced from time series , 2008, Proceedings of the National Academy of Sciences.

[14]  S. N. Dorogovtsev,et al.  Exactly solvable small-world network , 1999, cond-mat/9907445.

[15]  Ayfer Özgür,et al.  Hierarchical Cooperation Achieves Linear Capacity Scaling in Ad Hoc Networks , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[16]  Yutaka Shimada,et al.  Analysis of Chaotic Dynamics Using Measures of the Complex Network Theory , 2008, ICANN.

[17]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[18]  O. Rössler An equation for continuous chaos , 1976 .

[19]  Beom Jun Kim,et al.  Attack vulnerability of complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Steven H. Strogatz,et al.  Complex systems: Romanesque networks , 2005, Nature.

[21]  S. Havlin,et al.  Self-similarity of complex networks , 2005, Nature.

[22]  B. Luque,et al.  Horizontal visibility graphs: exact results for random time series. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M Small,et al.  Complex network from pseudoperiodic time series: topology versus dynamics. , 2006, Physical review letters.

[24]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[25]  Klaus Lehnertz,et al.  From brain to earth and climate systems: Small-world interaction networks or not? , 2011, Chaos.

[26]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[27]  Satoru Kawai,et al.  An Algorithm for Drawing General Undirected Graphs , 1989, Inf. Process. Lett..

[28]  M. Small,et al.  Characterizing pseudoperiodic time series through the complex network approach , 2008 .

[29]  David A. Rand,et al.  The bifurcations of duffing's equation: An application of catastrophe theory , 1976 .

[30]  Strozzi Fernanda,et al.  From Complex Networks to Time Series Analysis and Viceversa: Application to Metabolic Networks , 2009 .

[31]  Jürgen Kurths,et al.  Ambiguities in recurrence-based complex network representations of time series. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[33]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .

[34]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[35]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[36]  Lucas Lacasa,et al.  From time series to complex networks: The visibility graph , 2008, Proceedings of the National Academy of Sciences.

[37]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[38]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[39]  Shlomo Havlin,et al.  Origins of fractality in the growth of complex networks , 2005, cond-mat/0507216.

[40]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[41]  J. Kurths,et al.  Complex network approach for recurrence analysis of time series , 2009, 0907.3368.

[42]  Kazuyuki Aihara,et al.  Reproduction of distance matrices and original time series from recurrence plots and their applications , 2008 .

[43]  B. Bollobás The evolution of random graphs , 1984 .