One-side riddled basin below and beyond the blowout bifurcation

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 4, 2000, Pages

  Yang, H L ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); PHASE DIAGRAMS;

INVARIANT SUBSPACE (ISS); MAGNETOELASTICITY;

CHAOS THEORY;

EID: 0034296004     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.R4509     Document Type: Article

References (36)

1. H. Fujisaka, Prog. Theor. Phys. 70, 1264 (1983)
2. A. Pikovsky, Z. Phys. B: Condens. Matter 55, 149 (1984)
3. L.M. Pecora and T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)
4. Phys. Rev. Lett.N. Platt, E.A. Spiegel, and C. Tresser, 70, 279 (1993)
5. Phys. Rev. Lett.L. Yu, E. Ott, and Q. Chen, 65, 2935 (1990)
6. H.L. Yang, and E.J. Ding, Phys. Rev. E 50, R3295 (1994).
7. A.S. Pikovsky and P. Grassberger, J. Phys. A 24, 4587 (1991).
8. J.C. Alexander, J.A. Yorke, Z. You, and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992).
9. J.C. Sommerer and E. Ott, Nature (London) 365, 136 (1993)
10. E. Ott and J.C. Sommerer, Phys. Lett. A 188, 39 (1994).
11. P. Ashwin, J. Buescu, and I.N. Stewart, Phys. Lett. A 193, 126 (1994).
12. Y.C. Lai, C. Grebogi, J.A. Yorke, and S.C. Venkataramani, Phys. Rev. Lett. 77, 55 (1996).
13. S.C. Venkataramani, B.R. Hunt, E. Ott, Phys. Rev. E 54, 1346 (1996).
14. V. Astakhov, A. Shabunin, T. Kapitaniak, and V. Anishchenko, Phys. Rev. E 79, 1014 (1997).
15. Yu.L. Maistrenko, V.L. Maistrenko, A. Popovich, and E. Mosekilde, Phys. Rev. Lett. 80, 1638 (1998).
16. H.L. Yang and A.S. Pikovsky, Phys. Rev. E 60, 5474 (1999).
17. A. Popovich (unpublished).
18. N.F. Rulkov , Phys. Rev. E 51, 980 (1995)
19. Phys. Rev. EU. Parlitz , 54, 2115 (1996)
20. M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996)
21. Phys. Rev. Lett.M. Rosenblum, A. Pikovsky, and J. Kurths, 78, 4193 (1997).
22. J.P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).
23. B.R. Hunt and E. Ott, Phys. Rev. Lett. 76, 2254 (1996).
24. J. Milnor, Commun. Math. Phys. 99, 177 (1985).
25. C. Mira, L. Gardini, A. Barngola, and J.-C. Cathala, Chaotic Dynamics in Two-Dimensional Noninvertible Maps (World Scientific, Singapore, 1996).
26. The ending of this one-side riddled basin after the blowout bifurcation can be also different: the attractor goes away from the ISS and the ISS is no longer a part of the attractor’s boundary.
27. C. Grebogi, E. Ott, and J.A. Yorke, Phys. Rev. Lett. 50, 935 (1983)
28. C. GrebogiE. OttJ.A. YorkeErgodic Theory Dyn. Syst. 5, 341 (1985).
29. W.L. Ditto , Phys. Rev. Lett. 63, 923 (1989)
30. Phys. Rev. Lett.W.L. Ditto65, 533 (1990)
31. Phys. Rev. Lett.W.L. Ditto65, 3211 (1990)
32. Phys. Rev. Lett.W.L. Ditto66, 1947 (1991)
33. Phys. Rev. Lett.W.L. Ditto68, 2863 (1992)
34. Phys. Rev. Lett.W.L. Ditto74, 4420 (1995)
35. W.L. DittoPhys. Rev. A 46, 5253 (1992)
36. W.L. DittoPhys. Rev. E 51, R2689 (1995).