An automated algorithm for the generation of dynamically reconstructed trajectories

Chaos

Volumn 20, Issue 1, 2010, Pages

  Komalapriya, C ^a,b   Romano, M C ^c,d   Thiel, M ^c   Marwan, N ^b   Kurths, J ^b,c,e   Kiss, I Z ^f   Hudson, J L ^g  

^a UNIVERSITY OF POTSDAM   (Germany)

^b POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

^c UNIVERSITY OF ABERDEEN   (United Kingdom)

^d UNIVERSITY OF ABERDEEN   (United Kingdom)

^e HUMBOLDT UNIVERSITY   (Germany)

^f Saint Louis University   (United States)

^g University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; BIOTECHNOLOGY; INFORMATION PROCESSING; METHODOLOGY; NONLINEAR SYSTEM; PHYSICS; REPRODUCIBILITY; STATISTICAL ANALYSIS; STATISTICAL MODEL;

ALGORITHMS; BIOTECHNOLOGY; DATA COLLECTION; DATA INTERPRETATION, STATISTICAL; MODELS, STATISTICAL; NONLINEAR DYNAMICS; PHYSICS; REPRODUCIBILITY OF RESULTS;

EID: 79951986307     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3279680     Document Type: Article

References (40)

1. Ullner E, Koseska A, Kurths J, Volkov E, Kantz H, G-Ojalvo J. Phys. Rev. E 2008, 78:031904. PLEEE8, 1063-651X, 10.1103/PhysRevE.78.031904.
2. Pande VS, Baker I, Chapman J, Elmer SP, Khaliq S, Larson SM, Rhee YM, Shirts MR, Snow CD, Sorin EJ, Zagrovic B. Biopolymers 2003, 68:91. BIPMAA, 0006-3525, 10.1002/bip.10219.
3. Yorke JA, Yorke ED. J. Stat. Phys. 1979, 21:263. JSTPBS, 0022-4715, 10.1007/BF01011469.
4. Grebogi C, Ott E, Yorke JA. Phys. Rev. Lett. 1982, 48:1507. PRLTAO, 0031-9007, 10.1103/PhysRevLett.48.1507.
5. Grebogi C, Ott E, Yorke JA. Physica D 1983, 7:181. PDNPDT, 0167-2789, 10.1016/0167-2789(83)90126-4.
6. Kantz H, Grassberger P. Physica D 1985, 17:75. PDNPDT, 0167-2789, 10.1016/0167-2789(85)90135-6.
7. Tél T. Directions in Chaos 1990, 3. (World Scientific, Singapore, ).
8. Komalapriya C, Thiel M, Romano MC, Marwan N, Schwarz U, Kurths J. Phys. Rev. E 2008, 78:066217. PLEEE8, 1063-651X, 10.1103/PhysRevE.78.066217.
9. Poincaré H. Acta Math. 1890, 13:1. ACMAA8, 0001-5962.
10. Ott E. Chaos in Dynamical Systems 2002, 2nd ed. (Cambridge University Press, Cambridge, ).
11. Robinson G, Thiel M. Chaos 2009, 19:023104. CHAOEH, 1054-1500, 10.1063/1.3117151.
12. Grassberger P, Procaccia I. Phys. Rev. A 1983, 28:2591. PLRAAN, 1050-2947, 10.1103/PhysRevA.28.2591.
13. Dhamala M, Lai Y-C, Kostelich EJ. Phys. Rev. E 2001, 64:056207. PLEEE8, 1063-651X, 10.1103/PhysRevE.64.056207.
14. Kantz H, Schreiber T. Nonlinear Time Series Analysis 2004, and,, 2nd ed. (Cambridge University Press, Cambridge, ).
15. Marwan N, Romano MC, Thiel M, Kurths J. Phys. Rep., Phys. Lett. 2007, 438:237. PRPLCM, 0370-1573.
16. Fraser AM, Swinney HL. Phys. Rev. A 1986, 33:1134. PLRAAN, 1050-2947, 10.1103/PhysRevA.33.1134.
17. Thiel M, Romano MC, Read PL, Kurths J. Chaos 2004, 14:234. CHAOEH, 1054-1500, 10.1063/1.1667633.
18. Rössler OE. Phys. Lett. A 1976, 57:397. PYLAAG, 0375-9601, 10.1016/0375-9601(76)90101-8.
19. Hénon M. Commun. Math. Phys. 1976, 50:69. CMPHAY, 0010-3616, 10.1007/BF01608556.
20. Encyclopedia of Nonlinear Sciences 2005, (Taylor Francis, London, ).
21. Lorenz EN. J. Atmos. Sci. 1963, 20:130. JAHSAK, 0022-4928, 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
22. Gilmore R. Rev. Mod. Phys. 1998, 70:1455. RMPHAT, 0034-6861, 10.1103/RevModPhys.70.1455.
23. Nonhyperbolic dynamical systems are generally characterized by the existence of multiple main time scales (Refs. c17 c40). In the chaotic Rssler system, there exist two main time scales that characterize the dynamics. While the first time scale describes the short term dynamics of the attractor and is linked to the amplitude fluctuations of the system, the second one reflects the long term dynamics of the system and is related to the systems phase diffusion or relaxation behavior. The presence of two time scale dynamics can be identified either by analyzing the decay of autocorrelation functions envelope (Ref. c40) or the diagonal line distributions of a RP (Ref. c17).
24. Thiel M, Romano MC, Kurths J, Meucci R, Allaria E, Arecchi FT. Physica D 2002, 171:138. PDNPDT, 0167-2789, 10.1016/S0167-2789(02)00586-9.
25. Schinkel S, Dimigen O, Marwan N. Eur. Phys. J. Spec. Top. 2008, 164:45. ZZZZZZ, 1951-6355, 10.1140/epjst/e2008-00833-5.
26. Kiss IZ, Hudson JL. Phys. Chem. Chem. Phys. 2002, 4:2638. PPCPFQ, 1463-9076, 10.1039/b200716a.
27. Kiss IZ, Hudson JL. Phys. Rev. E 2001, 64:046215. PLEEE8, 1063-651X, 10.1103/PhysRevE.64.046215.
28. Kiss IZ, Wang W, Hudson JL. Phys. Chem. Chem. Phys. 2000, 2:3847. PPCPFQ, 1463-9076, 10.1039/b003812l.
29. Takens F. Dynamical Systems and Turbulence 1981, 898:366-381. 10.1007/BFb0091924, (Springer-Verlag, Berlin, ).
30. Crutchfield JP, Kaneko K. Phys. Rev. Lett. 1988, 60:2715. PRLTAO, 0031-9007, 10.1103/PhysRevLett.60.2715.
31. Eckhardt B, Mersmann A. Phys. Rev. E 1999, 60:509. PLEEE8, 1063-651X, 10.1103/PhysRevE.60.509.
32. Ott E, Tél T. Chaos 1993, 3:417. CHAOEH, 1054-1500, 10.1063/1.165949.
33. Toroczkai Z, Károlyi G, Péntek T, Tél T, Grebogi C. Phys. Rev. Lett. 1998, 80:500. PRLTAO, 0031-9007, 10.1103/PhysRevLett.80.500.
34. Dhamala M, Lai Y-C. Phys. Rev. E 1999, 59:1646. PLEEE8, 1063-651X, 10.1103/PhysRevE.59.1646.
35. Nusse HE, Yorke JA. Physica D 1989, 36:137. PDNPDT, 0167-2789, 10.1016/0167-2789(89)90253-4.
36. Jánosi IM, Flepp L, Tél T. Phys. Rev. Lett. 1994, 73:529. PRLTAO, 0031-9007, 10.1103/PhysRevLett.73.529.
37. Moresco P, Dawson SP. Physica D 1999, 126:38. PDNPDT, 0167-2789, 10.1016/S0167-2789(98)00234-6.
38. Sweet D, Nusse HE, Yorke JA. Phys. Rev. Lett. 2001, 86:2261. PRLTAO, 0031-9007, 10.1103/PhysRevLett.86.2261.
39. Dhamala M, Lai Y-C, Kostelich EJ. Phys. Rev. E 2000, 61:6485. PLEEE8, 1063-651X, 10.1103/PhysRevE.61.6485.
40. Anishchenko VS, Vadivasova TE, Okrokvertskhov GA, Strelkova GI. Phys. Usp. 2005, 48:151. PHUSEY, 1063-7869, 10.1070/PU2005v048n02ABEH002070.