High-dimensional interior crisis in the Kuramoto-Sivashinsky equation

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

Volumn 65, Issue 3, 2002, Pages

  Chian, A C L ^a,b   Rempel, E L ^a,b   Macau, E E ^b   Rosa, R R ^b   Christiansen, F ^c  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b INSTITUTO NACIONAL DE PESQUISAS ESPACIAIS   (Brazil)

^c DANISH METEOROLOGICAL INSTITUTE   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; CHAOS THEORY; DIFFUSION; PLASMA APPLICATIONS; TOKAMAK DEVICES; TURBULENCE; VISCOSITY;

CHAOTIC DYNAMICAL SYSTEMS; KURAMOTO-SIVASHINSKY (KS) EQUATIONS; PERIODIC BOUNDARY CONDITIONS; PHASE EVOLUTION;

NONLINEAR SYSTEMS;

EID: 41349096395     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.035203     Document Type: Article

References (42)

1. R.E. LaQuey, Phys. Rev. Lett. 34, 391 (1975);
2. B.I. Cohen, Nucl. Fusion 16, 971 (1976).
3. S.I. Itoh, Phys. Rev. Lett. 67, 2485 (1991);
4. S.I. Itoh, K. Itoh, and A. Fukuyama, Nucl. Fusion 33, 1445 (1993).
5. M.S. Benilov, Phys. Rev. A 45, 5901 (1992).
6. R. Erichsen, L.G. Brunnet, and F.B. Rizzato, Phys. Rev. E 60, 6566 (1999).
7. B. Bruhn and B.P. Koch, Phys. Rev. E 61, 3078 (2000);
8. B. Bruhn, Phys. Plasmas 8, 146 (2001).
9. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976).
10. P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, San Diego, 1990);T. Bohr et al., Dynamical Systems Approach to Turbulence (Cambridge University Press, Cambridge, 1998).
11. G.I. Sivashinsky, Acta Astron. 4, 1177 (1977).
12. G.I. Sivashinsky and D.M. Michelson, Prog. Theor. Phys. 63, 2112 (1980).
13. A.J. Babchin, Phys. Fluids 26, 3159 (1983).
14. M. Münkel and F. Kaiser, Physica D 98, 156 (1996).
15. C. Grebogi, E. Ott, and J.A. Yorke, Phys. Rev. Lett. 48, 1507 (1982);
16. C. GrebogiE. OttJ.A. YorkePhysica D 7, 181 (1983);
17. C. Grebogi, Phys. Rev. A 36, 5365 (1987);
18. K.G. Szabó, Phys. Rev. E 61, 5019 (2000);
19. C. Robert, Physica D 144, 44 (2000).
20. D. Dangoisse, P. Glorieux, and D. Hennequin, Phys. Rev. Lett. 57, 2657 (1986).
21. J.A. Hoffnagle, Phys. Rev. Lett. 61, 255 (1988).
22. W.L. Ditto, Phys. Rev. Lett. 63, 923 (1989).
23. R.W. Leven and M. Selent, Chaos, Solitons Fractals 4, 2217 (1994).
24. J.C. Sartorelli, W.M. Gonçalves, and R.D. Pinto, Phys. Rev. E 49, 3963 (1994);
25. Phys. Rev. ER.D. Pinto and J.C. Sartorelli, 61, 342 (2000).
26. A.C.-L. Chian, F.A. Borotto, and W.D. Gonzalez, Astrophys. J. 505, 993 (1998).
27. A. C.-L. Chian, F. A. Borotto, and E. L. Rempel, Int. J. Bifurcation Chaos (to be published).
28. Kaifen He, Phys. Rev. Lett. 80, 696 (1998);
29. Kaifen HePhys. Rev. E 59, 5278 (1999);
30. Kaifen HePhys. Rev. Lett. 84, 3290 (2000);
31. Kaifen HePhys. Rev. E 63, 016218 (2001).
32. C. Letellier, Phys. Rev. E 63, 042702 (2001).
33. P. Cvitanović, Phys. Rev. Lett. 61, 2729 (1988);
34. R. Artuso, E. Aurell, and P. Cvitanović, Nonlinearity 3, 325 (1990).
35. F. Christiansen, P. Cvitanović, and V. Putkaradze, Nonlinearity 10, 55 (1997).
36. A. Wolf, Physica D 16, 285 (1985).
37. S.W. Morris, Phys. Rev. Lett. 71, 2026 (1993).
38. K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer-Verlag, New York, 1996).
39. M.E. Johnson, M.S. Jolly, and I.G. Kevrekidis, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 1 (2001).
40. Z. You, E.J. Kostelich, and J.A. Yorke, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 605 (1991).
41. P.E. Bak, Phys. Rev. Lett. 83, 1339 (1999);
42. P.E. Bak, and R. Yoshiro, Contrib. Plasma Phys. 40, 227 (2000).