Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 89, Issue 3, 2014, Pages

  Liu, Jin Long ^a   Yu, Zu Guo ^a,b   Anh, Vo ^b  

^a XIANGTAN UNIVERSITY   (China)

^b QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

FRACTALS;

AVERAGE DEGREE; DEGREE DISTRIBUTIONS; FRACTAL ANALYSIS; FRACTAL PROPERTIES; FRACTIONAL BROWNIAN MOTION; TOPOLOGICAL PROPERTIES;

TOPOLOGY;

ALGORITHM; ANIMAL; BIOLOGICAL MODEL; COMPUTER SIMULATION; DIFFUSION; FRACTAL ANALYSIS; HUMAN; STATISTICAL MODEL;

ALGORITHMS; ANIMALS; COMPUTER SIMULATION; DIFFUSION; FRACTALS; HUMANS; MODELS, BIOLOGICAL; MODELS, STATISTICAL;

EID: 84898972614     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.89.032814     Document Type: Article

References (68)

1. R. Albert and A. L. Barabási, Rev. Mod. Phys. 74, 47 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.47
2. R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, Phys. Rev. E 81, 015101 (R) (2010). PLEEE8 1539-3755 10.1103/PhysRevE.81.015101
3. R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, New J. Phys. 12, 033025 (2010). NJOPFM 1367-2630 10.1088/1367-2630/12/3/033025
4. D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998). NATUAS 0028-0836 10.1038/30918 (Pubitemid 28292183)
5. A. L. Barabási and R. Albert, Science 286, 509 (1999). 10.1126/science.286.5439.509
6. M. E. J. Newman, SIAM Rev. 45, 167 (2003). SIREAD 0036-1445 10.1137/S003614450342480
7. M. Small, J. Zhang, and X. K. Xu, Lect. Notes Inst. Comput. Sci. Soc. Inf. Telecommun. Eng. 5, 2078 (2009). 9783-6420 10.1007/978-3-642-02469-6-84
8. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuño, Proc. Natl. Acad. Sci. USA 105, 4972 (2008). PNASA6 0027-8424 10.1073/pnas.0709247105 (Pubitemid 351738493)
9. B. Luque, L. Lacasa, F. Ballesteros, and J. Luque, Phys. Rev. E 80, 046103 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.80.046103
10. C. B. Li, H. Yang, and T. Komatsuzaki, Proc. Natl. Acad. Sci. USA 105, 536 (2008). PNASA6 0027-8424 10.1073/pnas.0707378105 (Pubitemid 351171743)
11. N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, and J. Kurths, Phys. Lett. A 373, 4246 (2009). PYLAAG 0375-9601 10.1016/j.physleta.2009.09.042
12. X. K. Xu, J. Zhang, and M. Small, Proc. Natl. Acad. Sci. USA 105, 19601 (2008). PNASA6 0027-8424 10.1073/pnas.0806082105
13. C. Liu and W. X. Zhou, J. Phys. A 43, 495005 (2010). 1751-8113 10.1088/1751-8113/43/49/495005
14. J. P. Eckmann, S. O. Kamphorst, and D. Ruelle, Europhys. Lett. 4, 973 (1987). EULEEJ 0295-5075 10.1209/0295-5075/4/9/004
15. J. P. Zbilut and C. L. Webber, Jr., Phys. Lett. A 171, 199 (1992). 10.1016/0375-9601(92)90426-M
16. C. L. Webber, Jr., and J. P. Zbilut, J. Appl. Physiol. 76, 965 (1994).
17. TOCSY: http://tocsy.pik-potsdam.de.
18. J. P. Zbilut, A. Giuliani, and C. L. Webber, Jr., Phys. Lett. A 246, 122 (1998). 10.1016/S0375-9601(98)00457-5
19. N. Marwan and J. Kurths, Phys. Lett. A 302, 299 (2002). PYLAAG 0375-9601 10.1016/S0375-9601(02)01170-2
20. M. C. Romano, M. Thiel, J. Kurths, and W. von Bloh, Phys. Lett. A 330, 214 (2004). PYLAAG 0375-9601 10.1016/j.physleta.2004.07.066
21. J. F. Donges, J. Heitzig, R. V. Donner, and J. Kurths, Phys. Rev. E 85, 046105 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.046105
22. R. V. Donner, J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, in Proceedings of the 2010 International Symposium on Nonlinear Theory and its Applications NOLTA2010 (Krakow 2010) (IEICE, Tokyo, 2010), pp. 87-90.
23. B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422 (1968). SIREAD 0036-1445 10.1137/1010093
24. L. Lacasa, B. Luque, J. Luque, and J. C. Nuño, Europhys. Lett. 86, 30001 (2009). EULEEJ 0295-5075 10.1209/0295-5075/86/30001
25. W. J. Xie and W. X. Zhou, Physica A 390, 3592 (2011). PHYADX 0378-4371 10.1016/j.physa.2011.04.020
26. Y. Zhou, Y. Leung, and Z. G. Yu, Phys. Rev. E 87, 012921 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.87.012921
27. M. A. Riley, R. Balasubramaniam, and M. T. Turvey, Gait Posture 9, 65 (1999). 0966-6362 10.1016/S0966-6362(98)00044-7 (Pubitemid 29173290)
28. J. S. Kim, K. I. Goh, G. Salvi, E. Oh, B. Kahng, and D. Kim, Phys. Rev. E 75, 016110 (2007). PLEEE8 1539-3755 10.1103/PhysRevE.75.016110 (Pubitemid 46191790)
29. B. G. Li, Z. G. Yu, and Y. Zhou, J. Stat. Mech.: Theor. Exp. (2014) P02020. 1742-5468 10.1088/1742-5468/2014/02/P02020
30. D. L. Wang, Z. G. Yu, and V. Anh, Chin. Phys. B 21, 080504 (2012). 1674-1056 10.1088/1674-1056/21/8/080504
31. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980). PRLTAO 0031-9007 10.1103/PhysRevLett.45.712
32. F. Takens, in Dynamical Systems and Turbulence, edited by D. A. Rand and L. S. Young, Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898, p. 366.
33. M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, Physica D 51, 52 (1991). PDNPDT 0167-2789 10.1016/0167-2789(91)90222-U
34. M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 73, 82 (1994). PDNPDT 0167-2789 10.1016/0167-2789(94)90226-7
35. A. M. Fraser and H. L. Swinney, Phys. Rev. A 33, 1134 (1986). 0556-2791 10.1103/PhysRevA.33.1134
36. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992). PLRAAN 1050-2947 10.1103/PhysRevA.45.3403
37. L. Y. Cao, Physica D 110, 43 (1997). PDNPDT 0167-2789 10.1016/S0167-2789(97)00118-8
38. N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, Phys. Rep. 438, 237 (2007). PRPLCM 0370-1573 10.1016/j.physrep.2006.11.001
39. M. A. Riley and G. C. Van Orden, Tutorials in contemporary nonlinear methods for the behavioral sciences, http://www.nsf.gov/sbe/bcs/pac/nmbs/nmbs. jsp.
40. P. Erdos and A. Rényi, Publ. Math. Debrecen 6, 290 (1959).
41. M. S. Roulston, Physica D 125, 285 (1999). PDNPDT 0167-2789 10.1016/S0167-2789(98)00269-3
42. Z. H. Tang and Z. G. Yu, Chin. J. Eng. Math. 29, 499 (2012).
43. D. F. Gleich, A graph library for Matlab based on the boost graph library, http://dgleich.github.com/matlab-bgl.
44. http://pajek.imfm.si/doku.php?id=pajek.
45. A.-L. Barabási and E. Bonabeau, Sci. Am. 288, 60 (2003). 10.1038/scientificamerican0503-60
46. X. H. Ni, Z. Q. Jiang, and W. X. Zhou, Phys. Lett. A 373, 3822 (2009). PYLAAG 0375-9601 10.1016/j.physleta.2009.08.041
47. R. Milo, S. S. Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Science 298, 824 (2002). SCIEAS 0036-8075 10.1126/science.298.5594.824 (Pubitemid 35231534)
48. R. Milo, S. Itzkovitz, N. Kashtan, R. Levitt, S. S. Orr, I. Ayzenshtat, M. Sheffer, and U. Alon, Science 303, 1538 (2004). SCIEAS 0036-8075 10.1126/science.1089167 (Pubitemid 38314428)
49. http://www.weizmann.ac.il/mcb/UriAlon/.
50. B. B. Mandelbrot, Science 156, 636 (1967). SCIEAS 0036-8075 10.1126/science.156.3775.636
51. J. Feder, Fractals (Plenum, New York, 1988).
52. B. B. Mandelbrot, The Fractal Geometry of Nature (Academic, New York, 1983).
53. G. Palla, I. Derenyi, I. Farkas, and T. Vicsek, Nature (London) 435, 814 (2005). NATUAS 0028-0836 10.1038/nature03607 (Pubitemid 40839731)
54. K. I. Goh, G. Salvi, B. Kahng, and D. Kim, Phys. Rev. Lett. 96, 018701 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.018701 (Pubitemid 43248420)
55. C. Song, S. Havlin, and H. A. Makse, Nature (London) 433, 392 (2005). NATUAS 0028-0836 10.1038/nature03248 (Pubitemid 40203314)
56. C. Song, L. K. Gallos, S. Havlin, and H. A. Makse, J. Stat. Mech.: Theor. Exp. (2007) P03006. 10.1088/1742-5468/2007/03/P03006
57. W. X. Zhou, Z. Q. Jiang, and D. Sornette, Physica A 375, 741 (2007). PHYADX 0378-4371 10.1016/j.physa.2006.10.025 (Pubitemid 44895636)
58. R. W. Floyd, Commun. ACM 5, 345 (1962). CACMA2 0001-0782 10.1145/367766.368168
59. R. V. Donner, J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, Eur. Phys. J. B 84, 653 (2011). EPJBFY 1434-6028 10.1140/epjb/e2011-10899-1
60. E. Canessa, J. Phys. A: Math. Gen. 33, 3637 (2000). JPHAC5 0305-4470 10.1088/0305-4470/33/19/302
61. V. V. Anh, Q. M. Tieng, and Y. K. Tse, Int. Trans. Oper. Res. 7, 349 (2000). 0969-6016 10.1111/j.1475-3995.2000.tb00204.x
62. Z. G. Yu, V. Anh, and K. S. Lau, Phys. Rev. E 64, 031903 (2001). 1063-651X 10.1103/PhysRevE.64.031903
63. Z. G. Yu, V. Anh, and K. S. Lau, Phys. Rev. E 68, 021913 (2003). 1063-651X 10.1103/PhysRevE.68.021913
64. Z. G. Yu, V. Anh, and K. S. Lau, J. Theor. Biol. 226, 341 (2004). JTBIAP 0022-5193 10.1016/j.jtbi.2003.09.009 (Pubitemid 37476181)
65. Z. G. Yu, V. V. Anh, K. S. Lau, and L.Q. Zhou, Phys. Rev. E 73, 031920 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.73.031920
66. Z. G. Yu, V. Anh, and R. Eastes, J. Geophys. Res. 114, A05214 (2009).
67. Z. G. Yu, V. Anh, Y. Wang, D. Mao, and J. Wanliss, J. Geophys. Res. 115, A10219 (2010). JGREA2 0148-0227 10.1029/2009JA015206
68. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Phys. Rev. A 33, 1141 (1986). 0556-2791 10.1103/PhysRevA.33.1141