Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls

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

Volumn 91, Issue 2, 2015, Pages

  Zou, Yong ^a,b,c   Donner, Reik V ^c   Kurths, Jürgen ^c,d,e,f  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b INSTITUTE OF THEORETICAL PHYSICS   (China)

^c POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

^d HUMBOLDT UNIVERSITY   (Germany)

^e UNIVERSITY OF ABERDEEN   (United Kingdom)

^f LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; FINANCIAL DATA PROCESSING; GAUSSIAN NOISE (ELECTRONIC); RANDOM PROCESSES;

CLIMATE VARIABLES; FINANCIAL TIME SERIES; FRACTIONAL BROWNIAN MOTION; FRACTIONAL GAUSSIAN NOISE (FGN); NETWORK PROPERTIES; NON-STATIONARITIES; NON-STATIONARY STOCHASTIC PROCESS; STATIONARY STOCHASTIC PROCESS;

STOCHASTIC SYSTEMS;

ALGORITHM; CHEMICAL MODEL; COMPUTER SIMULATION; FRACTAL ANALYSIS; MOTION; STATISTICS;

ALGORITHMS; COMPUTER SIMULATION; FRACTALS; MODELS, CHEMICAL; MOTION; STOCHASTIC PROCESSES;

EID: 84924368853     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.91.022926     Document Type: Article

References (38)

1. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 2004), 2nd ed.
2. J. C. Sprott, Chaos and Time-Series Analysis (Oxford University Press, Oxford, 2003).
3. H. Poincaré, Acta Mathematica 13, A271 (1890). 10.1007/BF02392514
4. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 2002), 2nd ed.
5. X. Xu, J. Zhang, and M. Small, Proc. Natl. Acad. Sci. USA 105, 19601 (2008). PNASA6 0027-8424 10.1073/pnas.0806082105
6. 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
7. 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
8. 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
9. J.-P. Eckmann, S. O. Kamphorst, and D. Ruelle, Europhys. Lett. 4, 973 (1987). EULEEJ 0295-5075 10.1209/0295-5075/4/9/004
10. B. Mandelbrot and J. Van Ness, SIAM Rev. 10, 422 (1968). SIREAD 0036-1445 10.1137/1010093
11. C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Phys. Rev. E 49, 1685 (1994). 1063-651X 10.1103/PhysRevE.49.1685
12. J. W. Kantelhardt, E. Koscielny-Bunde, H. H. Rego, S. Havlin, and A. Bunde, Physica A 295, 441 (2001). PHYADX 0378-4371 10.1016/S0378-4371(01)00144-3
13. K. Hu, P. C. Ivanov, Z. Chen, P. Carpena, and H. E. Stanley, Phys. Rev. E 64, 011114 (2001). 1063-651X 10.1103/PhysRevE.64.011114
14. A. Bunde and S. Havlin, Physica A 314, 15 (2002). PHYADX 0378-4371 10.1016/S0378-4371(02)01050-6
15. J. W. Kantelhardt, T. Penzel, S. Rostig, H. F. Becker, S. Havlin, and A. Bunde, Physica A 319, 447 (2003). PHYADX 0378-4371 10.1016/S0378-4371(02)01502-9
16. J.-L. Liu, Z.-G. Yu, and V. Anh, Phys. Rev. E 89, 032814 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.89.032814
17. J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, and J. Kurths, Proc. Natl. Acad. Sci. USA 108, 20422 (2011). PNASA6 0027-8424 10.1073/pnas.1117052108
18. J. F. Donges, R. V. Donner, K. Rehfeld, N. Marwan, M. H. Trauth, and J. Kurths, Nonlin. Proc. Geophys. 18, 545 (2011). 1607-7946 10.5194/npg-18-545-2011
19. 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
20. F. Strozzi, K. Poljansek, F. Bono, E. Gutiérrez, and J. ZaldIvar, Int. J. Bifurcation Chaos 21, 1047 (2011). IJBEE4 0218-1274 10.1142/S0218127411028891
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, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, and J. Kurths, Int. J. Bifurcation Chaos 21, 1019 (2011). IJBEE4 0218-1274 10.1142/S0218127411029021
23. Y. Zou, R. V. Donner, J. F. Donges, N. Marwan, and J. Kurths, Chaos 20, 043130 (2010). CHAOEH 1054-1500 10.1063/1.3523304
24. Y. Zou, R. V. Donner, and J. Kurths, Chaos 22, 013115 (2012). 10.1063/1.3677367
25. C. Grebogi, E. Ott, S. Pelikan, and J. A. Yorke, Physica D 13, 261 (1984). PDNPDT 0167-2789 10.1016/0167-2789(84)90282-3
26. U. Feudel, S. Kuznetsov, and A. Pikovsky, Strange Nonchaotic Attractors-Dynamics between Order and Chaos in Quasiperiodically Forced Systems (World Scientific, Singapore, 2006).
27. 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
28. F. Takens, in Dynamical Systems and Turbulence, Warwick 1980, Vol. 898 of Lecture Notes in Mathematics, edited by D. A. Rand and L.-S. Young (Springer, New York, 1981), pp. 366-381.
29. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992). PLRAAN 1050-2947 10.1103/PhysRevA.45.3403
30. A. M. Fraser and H. L. Swinney, Phys. Rev. A 33, 1134 (1986). 0556-2791 10.1103/PhysRevA.33.1134
31. P. Grassberger and I. Procaccia, Physica D 9, 189 (1983). PDNPDT 0167-2789 10.1016/0167-2789(83)90298-1
32. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, New York, 1982).
33. T. Gneiting and M. Schlather, SIAM Rev. 46, 269 (2004). SIREAD 0036-1445 10.1137/S0036144501394387
34. A. Witt and B. Malamud, Surveys Geophys. 34, 541 (2013). SUGEEC 0169-3298 10.1007/s10712-012-9217-8
35. R. V. Donner, J. F. Donges, Y. Zou, and J. H. Feldhoff, in Recurrence Quantification Analysis, edited by C. L. Webber, Jr. and N. Marwan (Springer International Publishing, Cham, 2015), Understanding Complex Systems, pp. 101-163.
36. D. Eroglu, N. Marwan, S. Prasad, and J. Kurths, Nonlin. Proc. Geophys. 21, 1085 (2014). 1607-7946 10.5194/npg-21-1085-2014
37. Y. Zou, J. Heitzig, R. V. Donner, J. F. Donges, J. D. Farmer, R. Meucci, S. Euzzor, N. Marwan, and J. Kurths, Europhys. Lett. 98, 48001 (2012). EULEEJ 0295-5075 10.1209/0295-5075/98/48001
38. J. Dall and M. Christensen, Phys. Rev. E 66, 016121 (2002). 1063-651X 10.1103/PhysRevE.66.016121