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Characterizing system dynamics with a weighted and directed network constructed from time series data
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1.
1. B. Kitchens, Symbolic Dynamics: One Sided, Two-Sided and Countable State Markov Shifts (Springer, 1998).
2.
2. J. Zhang and M. Small, “ Complex network from pseudoperiodic time series: Topology versus dynamics,” Phys. Rev. Lett. 96(23), 238701 (2006).
http://dx.doi.org/10.1103/PhysRevLett.96.238701
3.
3. J. Zhang, J. Sun, X. Luo, K. Zhang, T. Nakamura, and M. Small, “ Characterizing pseudoperiodic time series through the complex network approach,” Physica D 237(22), 28562865 (2008).
http://dx.doi.org/10.1016/j.physd.2008.05.008
4.
4. R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, and J. Kurths, “ Recurrence-based time series analysis by means of complex network methods,” Int. J. Bifurcation Chaos 21(04), 10191046 (2011).
http://dx.doi.org/10.1142/S0218127411029021
5.
5. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuño, “ From time series to complex networks: The visibility graph,” Proc. Natl. Acad. Sci. U.S.A. 105(13), 49724975 (2008).
http://dx.doi.org/10.1073/pnas.0709247105
6.
6. B. Luque, L. Lacasa, F. Ballesteros, and J. Luque, “ Horizontal visibility graphs: Exact results for random time series,” Phys. Rev. E 80(4), 046103 (2009).
http://dx.doi.org/10.1103/PhysRevE.80.046103
7.
7. L. Lacasa, A. Nunez, É. Roldán, J. M. R. Parrondo, and B. Luque, “ Time series irreversibility: A visibility graph approach,” Eur. Phys. J. B 85(6), 111 (2012).
http://dx.doi.org/10.1140/epjb/e2012-20809-8
8.
8. A. M. Nuñez, L. Lacasa, J. P. Gomez, and B. Luque, “ Visibility algorithms: A short review,” in New Frontiers in Graph Theory (InTech, Rijeka, 2012), pp. 119152.
9.
9. Y. Yang and H. Yang, “ Complex network-based time series analysis,” Physica A 387(5), 13811386 (2008).
http://dx.doi.org/10.1016/j.physa.2007.10.055
10.
10. Z. Gao and N. Jin, “ Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks,” Phys. Rev. E 79(6), 066303 (2009).
http://dx.doi.org/10.1103/PhysRevE.79.066303
11.
11. X. Xu, J. Zhang, and M. Small, “ Super family phenomena and motifs of networks induced from time series,” Proc. Natl. Acad. Sci. U.S.A. 105(50), 1960119605 (2008).
http://dx.doi.org/10.1073/pnas.0806082105
12.
12. Y. Shimada, T. Kimura, and T. Ikeguchi, “ Analysis of chaotic dynamics using measures of the complex network theory,” in ICANN (1), Vol. 5163 Lecture Notes in Computer Science, edited by V. Kurková, R. Neruda, and J. Koutník (Springer, 2008), p. 6170.
13.
13. N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, and J. Kurths, “ Complex network approach for recurrence analysis of time series,” Phys. Lett. A 373(46), 42464254 (2009).
http://dx.doi.org/10.1016/j.physleta.2009.09.042
14.
14. Z. Gao and N. Jin, “ Complex network from time series based on phase space reconstruction,” Chaos 19(3), 033137 (2009).
http://dx.doi.org/10.1063/1.3227736
15.
15. R. V Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, “ Recurrence networks: A novel paradigm for nonlinear time series analysis,” New J. Phys. 12(3), 033025 (2010).
http://dx.doi.org/10.1088/1367-2630/12/3/033025
16.
16. R. Xiang, J. Zhang, X.–K. Xu, and M. Small, “ Multiscale characterization of recurrence-based phase space networks constructed from time series,” Chaos 22, 013107 (2012).
http://dx.doi.org/10.1063/1.3673789
17.
17. G. Nicolis, A. Garcia Cantu, and C. Nicolis, “ Dynamical aspects of interaction networks,” Int. J. Bifurcation Chaos 15(11), 34673480 (2005).
http://dx.doi.org/10.1142/S0218127405014167
18.
18. A. H. Shirazi, G. Reza Jafari, J. Davoudi, J. Peinke, M. Reza Rahimi Tabar, and M. Sahimi, “ Mapping stochastic processes onto complex networks,” J. Stat. Mech. 2009(07), P07046.
http://dx.doi.org/10.1088/1742-5468/2009/07/P07046
19.
19. A. S. Campanharo, M. Irmak Sirer, R. Dean Malmgren, F. M. Ramos, and L. A. Nunes Amaral, “ Duality between time series and networks,” PloS One 6(8), e23378 (2011).
http://dx.doi.org/10.1371/journal.pone.0023378
20.
20. M. Small, “ Complex networks from time series: Capturing dynamics,” in 2013 IEEE International Symposium on Circuits and Systems (ISCAS) (IEEE, 2013), pp. 25092512.
21.
21.That is, replace the L numbers with a permutation of the integers such that the ith integer indicates the relative size of xi among the L numbers.
22.
22. C. Bandt and B. Pompe, “ Permutation entropy: A natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
http://dx.doi.org/10.1103/PhysRevLett.88.174102
23.
23. Y. Cao, W.-W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “ Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E 70(4), 46217 (2004).
http://dx.doi.org/10.1103/PhysRevE.70.046217
24.
24. M. Staniek and K. Lehnertz, “ Parameter selection for permutation entropy measurements,” Int. J. Bifurcation Chaos 17(10), 37293733 (2007).
http://dx.doi.org/10.1142/S0218127407019652
25.
25. D. Li, Z. Liang, Y. Wang, S. Hagihira, J. W. Sleigh, and X. Li, “ Parameter selection in permutation entropy for an electroencephalographic measure of isoflurane anesthetic drug effect,” J. Clin. Monit. Comput. 27(2), 113123 (2013).
http://dx.doi.org/10.1007/s10877-012-9419-0
26.
26. B. Fadlallah, B. Chen, A. Keil, and J. Príncipe, “ Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information,” Phys. Rev. E 87(2), 022911 (2013).
http://dx.doi.org/10.1103/PhysRevE.87.022911
27.
27. R. Donner, B. Scholz-Reiter, and U. Hinrichs, “ Nonlinear characterization of the performance of production and logistics networks,” J. Manuf. Syst. 27(2), 8499 (2008).
http://dx.doi.org/10.1016/j.jmsy.2008.10.001
28.
28. R. Donner, U. Hinrichs, and B. Scholz-Reiter, “ Symbolic recurrence plots: A new quantitative framework for performance analysis of manufacturing networks,” Eur. Phys. J. Spec. Top. 164(1), 85104 (2008).
http://dx.doi.org/10.1140/epjst/e2008-00836-2
29.
29. T. A. B. Snijders, “ The degree variance: An index of graph heterogeneity,” Social Networks 3(3), 163174, 1981.
http://dx.doi.org/10.1016/0378-8733(81)90014-9
30.
30. F. Fu, L.-H. Liu, and L. Wang, “ Evolutionary prisoner's dilemma on heterogeneous newman-watts small-world network,” Eur. Phys. J. B 56(4), 367372 (2007).
http://dx.doi.org/10.1140/epjb/e2007-00124-5
31.
31. H. D. Rozenfeld, J. E. Kirk, E. M. Bollt, and D. Ben-Avraham, “ Statistics of cycles: How loopy is your network?J. Phys. A: Math. Gen. 38(21), 4589 (2005).
http://dx.doi.org/10.1088/0305-4470/38/21/005
32.
32.We note that we do not claim that this estimate of the underlying distribution is unbiased. We will show that it is enough that it depends in some non-trivial way on the true distribution—and hence the true recurrence pattern of the underlying dynamical system.
33.
33. E. Mosekilde, Topics in Nonlinear Dynamics: Applications to Physics, Biology and Economic Systems (World Scientific, 1996).
34.
34. Y. Zou, R. V. Donner, M. Wickramasinghe, I. Z. Kiss, M. Small, and J. Kurths, “ Phase coherence and attractor geometry of chaotic electrochemical oscillators,” Chaos 22, 033130 (2012).
http://dx.doi.org/10.1063/1.4747707
35.
35. Y. Zou, R. V. Donner, J. F Donges, N. Marwan, and J. Kurths, “ Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods,” Chaos 20(4), 043130 (2010).
http://dx.doi.org/10.1063/1.3523304
36.
36. R. Hegger, H. Kantz, and T. Schreiber, “ Practical implementation of nonlinear time series methods: The tisean package,” Chaos 9(2), 413435 (1999).
http://dx.doi.org/10.1063/1.166424
37.
37. J. D. Noh, “ Loop statistics in complex networks,” Eur. Phys. J. B 66, 251257 (2008).
http://dx.doi.org/10.1140/epjb/e2008-00401-9
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/content/aip/journal/chaos/24/2/10.1063/1.4868261
2014-03-17
2014-07-28

Abstract

In this work, we propose a novel method to transform a time series into a weighted and directed network. For a given time series, we first generate a set of segments via a sliding window, and then use a doubly symbolic scheme to characterize every windowed segment by combining absolute amplitude information with an ordinal pattern characterization. Based on this construction, a network can be directly constructed from the given time series: segments corresponding to different symbol-pairs are mapped to network nodes and the temporal succession between nodes is represented by directed links. With this conversion, dynamics underlying the time series has been encoded into the network structure. We illustrate the potential of our networks with a well-studied dynamical model as a benchmark example. Results show that network measures for characterizing global properties can detect the dynamical transitions in the underlying system. Moreover, we employ a random walk algorithm to sample loops in our networks, and find that time series with different dynamics exhibits distinct cycle structure. That is, the relative prevalence of loops with different lengths can be used to identify the underlying dynamics.

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Scitation: Characterizing system dynamics with a weighted and directed network constructed from time series data
http://aip.metastore.ingenta.com/content/aip/journal/chaos/24/2/10.1063/1.4868261
10.1063/1.4868261
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