Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Chaos

Volumn 22, Issue 1, 2012, Pages

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

^a POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^c EAST CHINA NORMAL UNIVERSITY   (China)

^d HUMBOLDT UNIVERSITY   (Germany)

^e UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; COMPUTER SIMULATION; METHODOLOGY; NONLINEAR SYSTEM; OSCILLOMETRY;

ALGORITHMS; COMPUTER SIMULATION; NONLINEAR DYNAMICS; OSCILLOMETRY;

EID: 84859329357     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3677367     Document Type: Article

References (89)

1. Nayfeh A. Mook D. Nonlinear Oscillations 1979, and (Wiley, New York).
2. Guckenheimer J. Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1990, and 3rd ed. (Springer, New York).
3. Lichtenberg A. Lieberman M. Regular and Chaotic Dynamics 1992, and 2nd ed. (Springer, Berlin).
4. Rosenblum M.G. Pikovsky A.S. Kurths J. Phys. Rev. Lett. 1996, 76:1804. 10.1103/PhysRevLett.76.1804, and.
5. Pikovsky A. Rosenblum M. Kurths J. Synchronization-A Universal Concept in Nonlinear Sciences 2001, and (Cambridge University Press, Cambridge, England).
6. Wickramasinghe M. Kiss I.Z. Chaos 2010, 20:023125. 10.1063/1.3439209, and.
7. Kantz H. Schreiber T. Nonlinear Time Series Analysis 2004, and 2nd ed. (Cambridge University Press, Cambridge, England).
8. Sprott J.C. Chaos and Time-Series Analysis 2003, (Oxford University Press, Oxford).
9. Wolf A. Swift J. Swinney H. Vastano J. Physica D 1985, 16:285. 10.1016/0167-2789(85)90011-9, and.
10. Hilborn R. Chaos and Nonlinear Dynamics 2000, 2nd ed. (Oxford University Press, New York).
11. Rössler O.E. Phys. Lett. A 1976, 57:397. 10.1016/0375-9601(76)90101-8.
12. Romano M.C. Thiel M. Kurths J. Kiss I.Z. Hudson J. Europhys. Lett. 2005, 71:466. 10.1209/epl/i2005-10095-1, and.
13. Marwan N. Romano M. Thiel M. Kurths J. Phys. Rep. 2007, 438:237. 10.1016/j.physrep.2006.11.001, and.
14. Senthilkumar D.V. Srinivasan K. Murali K. Lakshmanan M. Kurths J. Phys. Rev. E 2010, 82:065201. 10.1103/PhysRevE.82.065201, and.
15. Suresh R. Senthilkumar D.V. Lakshmanan M. Kurths J. Phys. Rev. E 2010, 82:016215. 10.1103/PhysRevE.82.016215, and.
16. Eckmann J.-P. Kamphorst S.O. Ruelle D. Europhys. Lett. 1987, 4:973. 10.1209/0295-5075/4/9/004, and.
17. Zou Y. Pazó D. Romano M. Thiel M. Kurths J. Phys. Rev. E 2007, 76:016210. 10.1103/PhysRevE.76.016210, and.
18. Zou Y. Thiel M. Romano M. Kurths J. Chaos 2007, 17:043101. 10.1063/1.2785159, and.
19. Zou Y. Thiel M. Romano M. Read P. Kurths J. Eur. Phys. J. Spec. Top. 2008, 164:23. 10.1140/epjst/e2008-00831-7, and.
20. Rohde G.K. Nichols J.M. Dissinger B.M. Bucholtz F. Physica D 2008, 237:619. 10.1016/j.physd.2007.10.008, and.
21. Marwan N. Kurths J. Physica D 2009, 238:1711. 10.1016/j.physd.2009.04.018, and.
22. Zbilut J. Webber C. Phys. Lett. A 1992, 171:199. 10.1016/0375-9601(92)90426-M, and.
23. Webber C. Zbilut J. J. Appl. Physiol. 1994, 76:965. and.
24. Trulla L. Giuliani A. Zbilut J. Webber C. Phys. Lett. A 1996, 223:255. 10.1016/S0375-9601(96)00741-4, and.
25. Marwan N. Wessel N. Meyerfeldt U. Schirdewan A. Kurths J. Phys. Rev. E 2002, 66:026702. 10.1103/PhysRevE.66.026702, and.
26. Marwan N. Eur. Phys. J. Spec. Top. 2008, 164:3. 10.1140/epjst/e2008-00829-1.
27. Mackey M.C. Glass L. Science 1977, 197:287. 10.1126/science.267326, and.
28. Farmer J.D. Physica D 1982, 4:366. 10.1016/0167-2789(82)90042-2.
29. Balakrishnan V. Nicolis G. Nicolis C. J. Stat. Phys. 1997, 86:191. 10.1007/BF02180204, and.
30. Gao J.B. Phys. Rev. Lett. 1999, 83:3178. 10.1103/PhysRevLett.83.3178.
31. Balakrishnan V. Nicolis G. Nicolis C. Phys. Rev. E 2000, 61:2490. 10.1103/PhysRevE.61.2490, and.
32. Altmann E.G. da Silva E.C. Caldas I.L. Chaos 2004, 14:975. 10.1063/1.1795491, and.
33. Gao J.B. Cao Y.H. Gu L.Y. Harris J.G. Principe J.C. Phys. Lett. A 2003, 317:64. 10.1016/j.physleta.2003.08.018, and.
34. Rieke C. Andrzejak R.G. Mormann F. Lehnertz K. Phys. Rev. E 2004, 69:046111. 10.1103/PhysRevE.69.046111, and.
35. Rieke C. Sternickel K. Andrzejak R.G. Elger C.E. David P. Lehnert K. Phys. Rev. Lett. 2002, 88:244102. 10.1103/PhysRevLett.88.244102, and.
36. Altmann E.G. Kantz H. Phys. Rev. E 2005, 71:056106. 10.1103/PhysRevE.71.056106, and.
37. Baptista M. Ngamga E. Pinto P.R. Brito M. Kurths J. Phys. Lett. A 2010, 374:1135. 10.1016/j.physleta.2009.12.057, and.
38. Thiel M. Romano M. Kurths J. Appl. Nonlinear Dynam. 2003, 11:20. and.
39. Zhang J. Small M. Phys. Rev. Lett. 2006, 96:238701. 10.1103/PhysRevLett.96.238701, and.
40. Xu X. Zhang J. Small M. Proc. Natl. Acad. Sci. U.S.A. 2008, 105:19601. 10.1073/pnas.0806082105, and.
41. Yang Y. Yang H. Physica A 2008, 387:1381. 10.1016/j.physa.2007.10.055, and.
42. Lacasa L. Luque B. Ballesteros F. Luque J. Nuño J.C. Proc. Natl. Acad. Sci. U.S.A. 2008, 105:4972. 10.1073/pnas.0709247105, and.
43. Marwan N. Donges J.F. Zou Y. Donner R.V. Kurths J. Phys. Lett. A 2009, 373:4246. 10.1016/j.physleta.2009.09.042, and.
44. Donner R.V. Small M. Donges J.F. Marwan N. Zou Y. Xiang R. Kurths J. Int. J. Bifurcation Chaos Appl. Sci. Eng. 2011, 21:1019. 10.1142/S0218127411029021, and.
45. Donner R.V. Zou Y. Donges J.F. Marwan N. Kurths J. New J. Phys. 2010, 12:033025. 10.1088/1367-2630/12/3/033025, and.
46. Donner R.V. Donges J.F. Zou Y. Marwan N. Kurths J. Proceedings of the NOLTA 2010 2010, 87-90. and in (IEICE, Tokyo), pp.
47. Zou Y. Donner R.V. Donges J.F. Marwan N. Kurths J. Chaos 2010, 20:043130. 10.1063/1.3523304, and.
48. Donges J.F. Donner R.V. Rehfeld K. Marwan N. Trauth M.H. Kurths J. Nonlinear Processes Geophys. 2011, 18:545. 10.5194/npg-18-545-2011, and.
49. Donges J.F. Donner R.V. Trauth M.H. Marwan N. Schellnhuber H.J. Kurths J. Proc. Natl. Acad. Sci. U.S.A. 2011, 108:20422. 10.1073/pnas.1117052108, and.
50. Donner R.V. Heitzig J. Donges J.F. Zou Y. Marwan N. Kurths J. Eur. Phys. J. B 2011, 84:653. 10.1140/epjb/e2011-10899-1, and.
51. Donner R.V. Zou Y. Donges J.F. Marwan N. Kurths J. Phys. Rev. E 2010, 81:015101. 10.1103/PhysRevE.81.015101, and.
52. Facchini A. Kantz H. Phys. Rev. E 2007, 75:036215. 10.1103/PhysRevE.75.036215, and.
53. Gao Z. Jin N. Phys. Rev. E 2009, 79:066303. 10.1103/PhysRevE.79.066303, and.
54. Freeman L.C. Soc. Networks 1979, 1:215. 10.1016/0378-8733(78)90021-7.
55. Lathrop D. Kostelich E. Phys. Rev. A 1989, 40:4028. 10.1103/PhysRevA.40.4028, and.
56. Newman M. SIAM Rev. 2003, 45:167. 10.1137/S003614450342480.
57. Boccaletti S. Latora V. Moreno Y. Chavez M. Hwang D.U. Phys. Rep. 2006, 424:175. 10.1016/j.physrep.2005.10.009, and.
58. Costa L.F. Rodrigues F.A. Travieso G. Boas P.R. V. Adv. Phys. 2007, 56:167. 10.1080/00018730601170527, and.
59. Watts D.J. Strogatz S.H. Nature (London) 1998, 393:440. 10.1038/30918, and.
60. Barrat A. Weigt M. Eur. Phys. J. B 2000, 13:547. 10.1007/s100510050067, and.
61. Newman M.E. J. Phys. Rev. E 2001, 64:016131. 10.1103/PhysRevE.64.016131.
62. Newman M.E. J. Phys. Rev. Lett. 2002, 89:208701. 10.1103/PhysRevLett.89.208701.
63. Kralemann B. Cimponeriu L. Rosenblum M. Pikovsky A. Mrowka R. Phys. Rev. E 2007, 76:055201. 10.1103/PhysRevE.76.055201, and.
64. Kralemann B. Cimponeriu L. Rosenblum M. Pikovsky A. Mrowka R. Phys. Rev. E 2008, 77:066205. 10.1103/PhysRevE.77.066205, and.
65. Schwabedal J.T. C. Pikovsky A. Phys. Rev. E 2010, 81:046218. 10.1103/PhysRevE.81.046218, and.
66. Schwabedal J.T. C. Pikovsky A. Eur. Phys. J. Spec. Top. 2010, 187:63. 10.1140/epjst/e2010-01271-6, and.
67. Chen J.Y. Wong K.W. Shuai J.W. Phys. Lett. A 2001, 285:312. 10.1016/S0375-9601(01)00367-X, and.
68. Osipov G.V. Hu B. Zhou C. Ivanchenko M.V. Kurths J. Phys. Rev. Lett. 2003, 91:024101. 10.1103/PhysRevLett.91.024101, and.
69. Kiss I.Z. Lv Q. Hudson J.L. Phys. Rev. E 2005, 71:035201. 10.1103/PhysRevE.71.035201, and.
70. Boccaletti S. Allaria E. Meucci R. Phys. Rev. E 2004, 69:066211. 10.1103/PhysRevE.69.066211, and.
71. Fujisaka H. Yamada T. Kinoshita G. Kono T. Physica D 2005, 205:41. 10.1016/j.physd.2005.03.001, and.
72. Zakharova A.S. Vadivasova T.E. Anishchenko V.S. Int. J. Bifurcation Chaos Appl. Sci. Eng. 2008, 18:2877. 10.1142/S0218127408022147, and.
73. Pikovsky A.S. Kurths J. Phys. Rev. Lett. 1997, 78:775. 10.1103/PhysRevLett.78.775, and.
74. Zhou C.S. Kurths J. Allaria E. Boccaletti S. Meucci R. Arecchi F.T. Phys. Rev. E 2003, 67:066220. 10.1103/PhysRevE.67.066220, and.
75. Montgomery D.C. Design and Analysis of Experiments 2009, 7th ed. (Wiley, New York).
76. Conover W.J. Practical Nonparametric Statistics 1999, (Wiley, New York).
77. Hollander M. Wolfe D.A. Nonparametric Statistical Methods 1999, and 2nd ed. (Wiley, New York).
78. Lomax R.G. Statistical Concepts: A Second Course for Education and the Behavioral Sciences 2007, (Lawrence Erlbaum Associates Inc., Mahwah, NJ).
79. Gaspard P. Nicolis G. J. Stat. Phys. 1983, 31:499. 10.1007/BF01019496, and.
80. Gaspard P. Kapral R. Nicolis G. J. Stat. Phys. 1984, 35:697. 10.1007/BF01010829, and.
81. Kahan S. Sicardi-Schifino A.C. Physica A 1999, 262:144. 10.1016/S0378-4371(98)00389-6, and.
82. Genesio R. Innocenti G. Gualdani F. Phys. Lett. A 2008, 372:1799. 10.1016/j.physleta.2007.10.063, and.
83. Barrio R. Blesa F. Serrano S. Physica D 2009, 238:1087. 10.1016/j.physd.2009.03.010, and.
84. Rössler O.E. Ann. N.Y. Acad. Sci. 1979, 316:376. 10.1111/j.1749-6632.1979.tb29482.x.
85. Sprott J.C. Linz S.J. Int. J. Chaos Theory Appl. 2000, 5:3. and.
86. Glass L. Mackey M.C. Ann. N.Y. Acad. Sci. 1979, 316:214. 10.1111/j.1749-6632.1979.tb29471.x, and.
87. Senthilkumar D.V. Marwan N. Kurths J. Proceedings of the NOLTA 2010 2010, 83-86. and in (IEICE, Tokyo), pp.
88. Csárdi G. Nepusz T. InterJournal 2006, CX.18:1695. and.
89. Note that T is sometimes referred to as the (Barrat-Weigt) global clustering coefficient, often also denoted as e.g., in Ref. 47. In order to avoid confusion, in this work, we prefer to discuss both measures separately.