Devaney's chaos on recurrence plots

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

Volumn 82, Issue 3, 2010, Pages

  Hirata, Yoshito ^a   Aihara, Kazuyuki ^a  

^a INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DETERMINISTIC CHAOS; DEVANEY'S CHAOS; FINITE LENGTH; RECURRENCE PLOT;

DYNAMICAL SYSTEMS; TIME SERIES;

CHAOS THEORY;

EID: 78651240473     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.036209     Document Type: Article

References (27)

1. R. L. Devaney, An Introduction to Chaotic Dynamical Systems (Addison-Wesley, Reading, Massachusetts, 1989).
2. J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacy, Am. Math. Monthly 99, 332 (1992). 10.2307/2324899
3. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, England, 1997).
4. M. Small, Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance (World Scientific, New Jersey, 2005).
5. J. A. Scheinkman and B. LeBaron, J. Business 62, 311 (1989). 10.1086/296465
6. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, Physica D 58, 77 (1992). 10.1016/0167-2789(92)90102-S
7. T. Schreiber and A. Schmitz, Phys. Rev. Lett. 77, 635 (1996). 10.1103/PhysRevLett.77.635
8. M. Small, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 87, 188101 (2001). 10.1103/PhysRevLett.87.188101
9. M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985). 10.1103/PhysRevLett.55.1082
10. M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Physica D 65, 117 (1993). 10.1016/0167-2789(93)90009-P
11. H. Kantz, Phys. Lett. A 185, 77 (1994). 10.1016/0375-9601(94)90991-1
12. T. Tanaka, K. Aihara, and M. Taki, Phys. Rev. E 54, 2122 (1996). 10.1103/PhysRevE.54.2122
13. T. Ikeguchi and K. Aihara, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 1267 (1997). 10.1142/S0218127497001011
14. T. Tanaka, K. Aihara, and M. Taki, Physica D 111, 42 (1998). 10.1016/S0167-2789(97)80004-8
15. M. Paluš, Nonlinear Analysis of Physiological Data, edited by, H. Kantz,,, J. Kurths,, and, G. Mayer-Kress, (Springer, Berlin, Germany, 1998), pp. 49-66.
16. G. A. Gottwald and I. Melbourne, Proc. R. Soc. London, Ser. A 460, 603 (2004). 10.1098/rspa.2003.1183
17. J. Hu, W.-W. Tung, J. Gao, and Y. Cao, Phys. Rev. E 72, 056207 (2005). 10.1103/PhysRevE.72.056207
18. G. A. Gottwald and I. Melbourne, Phys. Rev. E 77, 028201 (2008). 10.1103/PhysRevE.77.028201
19. N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, Phys. Rep. 438, 237 (2007). 10.1016/j.physrep.2006.11.001
20. A. Mees, K. Aihara, M. Adachi, K. Judd, T. Ikeguchi, and G. Matsumoto, Phys. Lett. A 169, 41 (1992). 10.1016/0375-9601(92)90802-S
21. Y. Hirata, K. Judd, and K. Aihara, Phys. Lett. A 346, 141 (2005). 10.1016/j.physleta.2005.07.081
22. M. Thiel, M. C. Romano, and J. Kurths, Phys. Lett. A 330, 343 (2004). 10.1016/j.physleta.2004.07.050
23. Y. Hirata, S. Horai, and K. Aihara, Eur. Phys. J. Spec. Top. 164, 13 (2008). 10.1140/epjst/e2008-00830-8
24. E. Bradley and R. Mantilla, Chaos 12, 596 (2002). 10.1063/1.1488255
25. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992). 10.1103/PhysRevA.45.3403
26. R. Hegger, H. Kantz, and T. Schreiber, Chaos 9, 413 (1999). 10.1063/1.166424
27. M. Paluš, J. Kurths, U. Schwarz, D. Novatná, and I. Charvátová, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 2519 (2000). 10.1142/S0218127400001766