Theory of pattern forming systems under traveling-wave forcing

Physics Reports

Volumn 447, Issue 3-6, 2007, Pages 73-111

  Rüdiger, Sten ^a,b   Nicola, Ernesto M ^c   Casademunt, Jaume ^d   Kramer, Lorenz ^e  

^a HUMBOLDT UNIVERSITY   (Germany)

^b HAHN MEITNER INSTITUT   (Germany)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^d UNIVERSITY OF BARCELONA   (Spain)

^e UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Amplitude equations; Hexagonal patterns; Kinks; Modulational instabilities; Pattern formation; Phase diffusion; Pulses; Resonance; Spatio temporal forcing; Traveling wave forcing; Turing patterns

Indexed keywords

EID: 34347263032     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2007.02.017     Document Type: Review

References (77)

1. Cross M.C., and Hohenberg P.C. Rev. Mod. Phys. 65 (1993) 851
2. Walgraef D. Spatio-Temporal Pattern Formation (1997), Springer, New York
3. Pikovsky A., Rosenblum M., and Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences (2003), Cambridge University Press
4. Mikhailov A.S., and Showalter K. Phys. Rep. 425 (2006) 79
5. Coullet P., Lega J., Houchmanzadeh B., and Lajzerowics J. Phys. Rev. Lett. 65 (1990) 1352-1355
6. Coullet P., and Emilsson K. Physica D 61 (1992) 119-131
7. Petrov V., Ouyang Q., and Swinney H.L. Nature 388 (1997) 655-657
8. Elphick C., Hagberg A., and Meron E. Phys. Rev. Lett. 80 (1998) 5007
9. Lin A.L., Bertram M., Martinez K., Swinney H.L., Ardalea A., and Carey G.F. Phys. Rev. Lett. 84 (2000) 4240
10. Lin A.L., Hagberg A., Ardelea A., Bertram M., Swinney H.L., and Meron E. Phys. Rev. E 62 (2000) 3790
11. Park H.-K. Phys. Rev. Lett. 86 (2001) 1130
12. Yochelis A., Hagberg A., Meron E., Lin A.L., and Swinney H.L. Siam J. Appl. Dyn. Sys. 1 (2002) 236
13. Yochelis A., Elphick C., Hagberg A., and Meron E. Physica D 199 (2004) 201
14. Lin A.L., Hagberg A., Meron E., and Swinney H.L. Phys. Rev. E 69 (2004) 066217
15. Chaté H., Pikovsky A., and Rudzick O. Physica 131D (1999) 17
16. Argentina M., Rudzick O., and Velarde M.G. Chaos 14 (2004) 777
17. Rudzick O., and Mikhailov A.S. Phys. Rev. Lett. 96 (2006) 018302
18. Zhang W., and Viñals J. J. Fluid Mech. 336 (1997) 301-330
19. Horvath A.K., Dolnik M., Muñuzuri A.P., Zhabotinsky A.M., and Epstein I.R. Phys. Rev. Lett. 83 (1999) 2950-2952
20. Dolnik M., Zhabotinsky A.M., and Epstein I.R. Phys. Rev. E 63 (2001) 026101
21. Careta A., and Sagues F. J. Chem. Phys. 92 (1990) 1098-1105
22. Lowe M., Gollub J.P., and Lubensky T.C. Phys. Rev. Lett. 51 (1983) 786-789
23. Lowe M., and Gollub J.P. Phys. Rev. A 31 (1985) 3893-3897
24. Lowe M., Albert B.S., and Gollub J.P. J. Fluid Mech. 173 (1986) 253-272
25. Coullet P. Phys. Rev. Lett. 56 (1986) 724
26. Coullet P., and Huerre P. Physica D 23 (1986) 27-44
27. Coullet P., and Repaux D. Europhys. Lett. 3 (1987) 573-579
28. Coullet P., Elphick D., and Repaux D. Phys. Rev. Lett. 58 (1987) 431
29. Elphick C., Meron E., and Spiegel E.A. Phys. Rev. Lett. 61 (1988) 496
30. Coullet P., and Walgraef D. Europhys. Lett. 10 (1989) 525-531
31. Pismen L.M. Phys. Rev. Lett. 59 (1987) 2740-2743
32. Dolnik M., Berenstein I., Zhabotinsky A.M., and Epstein I.R. Phys. Rev. Lett. 87 (2001) 238301
33. Yang L., Dolnik M., Zhabotinsky A.M., and Epstein I.R. Phys. Rev. Lett. 88 (2002) 208303
34. Semwogerere D., and Schatz M.F. Phys. Rev. Lett. 88 (2002) 054501
35. Neubecker R., and Zimmermann A. Phys. Rev. E 65 (2002) 035205
36. Henriot M., Burguete J., and Ribotta R. Phys. Rev. Lett. 91 (2003) 104501
37. Peter R., Hilt M., Ziebert F., Bammert J., Erlenkämper C., Lorscheid N., Weitenberg C., Winter A., Hammele M., and Zimmermann W. Phys. Rev. E 71 (2005) 046212
38. J.H. McCoy, W. Brunner, W. Pesch, E. Bodenschatz, 2006, preprint.
39. Hammele M., and Zimmermann W. Phys. Rev. E 73 (2006) 066211
40. Rüdiger S., Míguez D.G., Muñuzuri A.P., Sagués F., and Casademunt J. Phys. Rev. Lett. 90 (2003) 128301
41. Utzny C., Zimmermann W., and Bär M. Europhys. Lett. 57 (2002) 113
42. Míguez D.G., Nicola E.M., Muñuzuri A.P., Casademunt J., Sagués F., and Kramer L. Phys. Rev. Lett. 93 (2004) 048303
43. Sagués F., Míguez D.G., Nicola E.M., Munũzuri A.P., Casademunt J., and Kramer L. Physica D 199 (2004) 235
44. Rüdiger S., Casademunt J., and Kramer L. Disc. Cont. Dyn. Syst. B 5 (2005) 1027
45. Míguez D.G., Pérez-Villar V., and Muñuzuri A.P. Phys. Rev. E 71 (2005) 066217
46. Berenstein I., and Muñuzuri A.P. Phys. Rev. E 74 (2006) 036202
47. S. Rüdiger, J. Casademunt, L. Kramer, Phys. Rev. Lett. (2007), to appear.
48. Coullet P., Riera C., and Tresser C. Chaos 14 (2004) 193
49. Coullet P., Toniolo C., and Tresser C. Chaos 14 (2004) 839
50. Schuler S., Hammele M., and Zimmermann W. Eur. Phys. J. B 42 (2004) 591
51. Zykov S., Zykov V.S., and Davydov V. Europhys. Lett. 73 (2006) 335-341
52. Ohta T., and Tokuda H. Phys. Rev. E 72 (2005) 046216
53. Tokuda H., and Ohta T. Progr. Theor. Phys. 161 Suppl. (2006) 368
54. Tokuda H., and Ohta T. J. Phys. Soc. Japan 75 (2006) 064005
55. Vanag V.K., and Epstein I.R. Phys. Rev. E 67 (2003) 066219
56. Míguez D.G., Dolnik M., Muñuzuri A.P., and Kramer L. Phys. Rev. Lett. 96 (2006) 048304
57. Míguez D.G., Satnoianu R.A., and Muñuzuri A.P. Phys. Rev. E 73 (2006) 025201R
58. Lengyel I., Rábai G., and Epstein I.R. J. Am. Chem. Soc. 112 (1990) 4606-4607
59. Muñuzuri A.P., Dolnik M., Zhabotinsky A.M., and Epstein I.R. J. Am. Chem. Soc. 121 (1999) 8065-8069
60. Turing A.M. Philos. Trans. R. Soc. London B 237 (1952) 37
61. Castets V., Dulos E., Boissonade J., and De Kepper P. Phys. Rev. Lett. 64 (1990) 2953-2956
62. Ouyang Q., and Swinney H.L. Nature 352 (1991) 610-612
63. R. Kapral, K. Showalter (Eds.), Chemical Waves and Patterns, Kluwer Academic Publishers, Dordrecht, 1995.
64. Kadar S., Wang J., and Showalter K. Nature 391 (1998) 770
65. Sendiña-Nadal I., Alonso S., Pérez-Muñuzuri V., Gómez-Gesteira M., Pérez-Villar V., Ramírez-Piscina L., Casademunt J., Sancho J.M., and Sagués F. Phys. Rev. Lett. 84 (2000) 2734
66. Gambaudo J.M. J. Differential Equations 65 (1985) 172-199
67. Strogatz S.H. Nonlinear Dynamics and Chaos (1994), Addison-Wesley, Reading, MA
68. E.J. Doedel, A.R. Champneys, T.F. Fairgrieve, Yu.A. Kuznetsov, B. Sandstede, X. Wang (1997) AUTO97 (with HomCont), Technical Report, Concordia University, 1997.
69. B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students, SIAM, 2002.
70. Skryabin D.V., Yulin A., Michaelis D., Firth W.J., Oppo G.-L., Peschel U., and Lederer F. Phys. Rev. E 64 (2001) 056618
71. Pismen L.M. Chaotic wave trains. Phys. Rev. A 39 (1989) 6604
72. Levi M., Hoppenstedt F., and Miranker W. Quart. Appl. Math. 35 (1978) 167
73. Kupferman R., Kaiser M., Schuss Z., and Ben-Jacob E. Phys. Rev. A 45 (1992) 745
74. Krekhov A., and Kramer L. Phys. Rev. E 70 (2004) 061801
75. Coullet P., Riera C., and Tresser C. Chaos 14 (2004) 193-198
76. Barland S., Tredicce J.R., Brambilla M., Lugiato L.A., Balle S., Giudici M., Maggipinto T., Spinelli L., Tissoni G., Knodl T., Miller M., and Jager R. Nature 419 (2002) 699-702
77. Kaminaga A., Vanag V.K., and Epstein I.R. Angew. Chem. Int. Ed. 45 (2006) 3087-3089