Controlling turbulence in the complex Ginzburg-Landau equation II. Two-dimensional systems

Physica D: Nonlinear Phenomena

Volumn 106, Issue 3-4, 1997, Pages 327-362

  Battogtokh, D ^a,b,c   Preusser, A ^a   Mikhailov, A ^a  

^a FRITZ HABER INSTITUT DER MAX PLANCK GESELLSCHAFT   (Germany)

^b KYOTO UNIVERSITY   (Japan)

^c INSTITUTE OF CHEMISTRY AND CHEMICAL TECHNOLOGY   (Mongolia)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; FEEDBACK; FEEDBACK CONTROL; TURBULENCE;

COMPLEX GINZBURG-LANDAU EQUATION; GLOBAL FEEDBACKS; OSCILLATORY DISTRIBUTED SYSTEMS; PHASE; TWO DIMENSIONAL SYSTEMS;

OSCILLATIONS;

EID: 0031209292     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00046-8     Document Type: Article

References (37)

1. A. Newell, Lect. Appl. Math. 15 (1974) 157.
2. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 54 (1975) 687;
3. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55 (1976) 356.
4. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
5. A.S. Mikhailov and I.V. Uporov, Dokl. Acad. Nauk SSSR 249 (1979) 733.
6. J.M. Greenberg, SIAM J. Appl. Math. 39 (1980) 301;
7. Adv. Appl. Math. 42 (1981) 450.
8. P.C. Hagan, SIAM J. Appl. Math. 42 (1982) 762.
9. N. Bekki and K. Nozaki, Phys. Lett. A 110 (1985) 133.
10. P. Coullet, L. Gil and J. Lega, Phys. Rev. Lett. 62 (1989) 1619.
11. T. Bohr, A.W. Pedersen and M.H. Jensen, Phys. Rev. A 42 (1990) 3626.
12. E. Bodenshatz, M. Kaiser, L. Kramer, W. Pesch, A. Weber and W. Zimmermann, in: New Trends in Nonlinear Dynamics and Pattern Forming Phenomena, eds. P. Coullet and P. Huerre (Plenum Press, New York, 1990).
13. B.I. Shraiman, A. Pumir, W. van Saarloos, P.C. Hohenberg, H. Chaté and M. Holen, Physica D 57 (1992) 241.
14. I. Aranson, L. Kramer and A. Weber, Phys. Rev. E 47 (1993) 3231.
15. H. Chaté and P. Manneville, Physica A 224 (1996) 348.
16. A.S. Mikhailov and A.Yu Loskutov, Foundations of Synergetics II. Chaos and Noise, 2nd enlarged edn. (Springer, Berlin, 1996).
17. L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon, Oxford, 1980).
18. D. Walgraef, G. Dewel and P. Borkmans, Phys. Rev. A 21 (1980) 397.
19. A.S. Mikhailov, Foundations of Synergetics I. Distributed Active Systems, 2nd revised edn. (Springer, Berlin, 1994).
20. D. Battogtokh and A.S. Mikhailov, Physica D 90 (1996) 84.
21. R. Imbihl and G. Ertl, Chem. Rev. 95 (1995) 697.
22. H. Levine and X. Zou, Phys. Rev. Lett. 69 (1992) 204.
23. G. Veser, F. Mertens, A.S. Mikhailov and R. Imbihl, Phys. Rev. Lett. 71 (1993) 935.
24. F. Mertens, R. Imbihl and A.S. Mikhailov, J. Chem. Phys. 99 (1993) 8668.
25. F. Mertens, R. Imbihl and A.S. Mikhailov, J. Chem. Phys. 101 (1994) 9903.
26. M. Falke, H. Engel and M. Neufeld, Phys. Rev. E 52 (1995) 763.
27. K. Rose, D. Battogtokh, A.S. Mikhailov, R. Imbihl, W. Engel and A. Bradshaw, Phys. Rev. Lett. 76 (1996) 3582.
28. D. Battogtokh, A. Preusser and A.S. Mikhailov, Computer videos of turbulence in CGLE with global feedback, in: http://www.fhi-berlin.mpg.de/~complsys.
29. P. Coullet and K. Emilsson, Physica D 61 (1992) 119.
30. P. Coullet and K. Emilsson, Physica A 88 (1992) 190.
31. P. Ortoleva and J. Ross, J. Chem. Phys. 58 (1973) 5673.
32. H. Chaté and P. Mannevile, Phys. Lett. A 171 (1992) 183.
33. S. Popp, O. Stiller, I. Aranson and L. Kramer, Physica D 84 (1995) 424.
34. I. Aranson, L. Kramer and A. Weber, Phys. Rev. Lett. 72 (1994) 2316.
35. G. Veser, F. Esch and R. Imbihl, Catal. Lett. 13 (1992) 371.
36. M. Bazhenov, T. Bohr, K. Gorshkov and M. Rabinovich, Phys. Lett. A 217 (1996) 104.
37. H. Chaté, Nonlinearity 7 (1994) 185.