Localized patterns in reaction-diffusion systems

Chaos

Volumn 17, Issue 3, 2007, Pages

  Vanag, Vladimir K ^a   Epstein, Irving R ^a  

^a BRANDEIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34848916339     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2752494     Document Type: Article

References (121)

1. E. S. Lobanova, E. E. Shnol, and F. I. Ataullakhanov, Phys. Rev. E 70, 032903 (2004).
2. E. S. Lobanova and F. I. Ataullakhanov, Phys. Rev. Lett. 91, 138301 (2003).
3. P. Jung and J. Milton, Epilepsy as a Dynamical Disease (Springer, New York, 2003).
4. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jager, Nature 419, 699 (2002).
5. P. Coullet, C. Riera, and C. Tresser, Chaos 14, 193 (2004).
6. A. Kaminaga, V. K. Vanag, and I. R. Epstein, Angew. Chem., Int. Ed. 45, 3087 (2006).
7. B. Schapers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
8. M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 73, 640 (1994).
9. V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 92, 128301 (2004).
10. V. K. Vanag and I. R. Epstein, Phys. Rev. E 73, 016201 (2006).
11. M. Bode, A. W. Liehr, C. P. Schenk, and H. G. Purwins, Physica D 161, 45 (2002).
12. Y. Nishiura, T. Teramoto, and K. I. Ueda, Chaos 15, 047509 (2005).
13. A. T. Winfree, Science 175, 634 (1972).
14. A. N. Zaikin and A. M. Zhabotinsky, Nature 225, 535 (1970).
15. V. Castets, E. Dulos, J. Boissonade, and P. De Kepper, Phys. Rev. Lett. 64, 2953 (1990).
16. V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 87, 228301 (2001).
17. A. M. Turing, Philos. Trans. R. Soc. London, Ser. A 237, 37 (1952).
18. V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. 88, 088303 (2002).
19. S. Bouzat and H. S. Wio, Phys. Lett. A 268, 323 (2000).
20. G. Dewel, P. Borckmans, A. Dewit, B. Rudovics, J. J. Perraud, E. Dulos, J. Boissonade, and P. Dekepper, Physica A 213, 181 (1995).
21. J. S. Park and K. J. Lee, Phys. Rev. E 73, 066219 (2006).
22. N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett. 15, 240 (1965).
23. N. J. Doran and K. J. Blow, IEEE J. Quantum Electron. 19, 1883 (1983).
24. Focus issue on " Nonlinear localized modes: Physics and applications., " Chaos 13, issue 2 (2003), edited by, Yu. S. Kivshar, and, S. Flach,.
25. Yu. S. Kivshar and S. Flach, Chaos 13, 586 (2003).
26. S. Koga and Y. Kuramoto, Prog. Theor. Phys. 63, 106 (1980).
27. B. S. Kerner and V. V. Osipov, Autosolitons: A New Approach to Problems of Self-Organization and Turbulence (Kluwer, Dordrecht, 1994).
28. C. B. Muratov and V. V. Osipov, Phys. Rev. E 53, 3101 (1996).
29. J. J. Niemela, G. Ahlers, and D. S. Cannell, Phys. Rev. Lett. 64, 1365 (1990).
30. O. Lioubashevski, H. Arbell, and J. Fineberg, Phys. Rev. Lett. 76, 3959 (1996).
31. H. Jamgotchian, N. Bergeon, D. Benielli, Ph. Voge, B. Billia, and R. Guerin, Phys. Rev. Lett. 87, 166105 (2001).
32. Yu. A Astrov, E. Ammelt, and H.-G. Purwins, Phys. Rev. Lett. 78, 3129 (1997).
33. Yu. A. Astrov and Yu. A. Logvin, Phys. Rev. Lett. 79, 2983 (1997).
34. F. J. Niedernostheide, B. S. Kerner, and H. G. Purwins, Phys. Rev. B 46, 7559 (1992).
35. P. B. Umbanhowar, F. Melo, and H. L. Swinney, Nature 382, 793 (1996).
36. L. Stenflo and M. Y. Yu, Phys. Plasmas 10, 912 (2003).
37. V. B. Taranenko, G. Slekys, and C. O. Weiss, Chaos 13, 777 (2003).
38. N. N. Rozanov, Opt. Spectrosc. 96, 569 (2004).
39. N. N. Rozanov, Phys. Usp. 48, 167 (2005).
40. N. N. Rozanov, Opt. Spectrosc. 102, 255 (2007).
41. V. K. Vanag and D. V. Boulanov, J. Phys. Chem. 98, 1449 (1994).
42. I. R. Epstein and V. K. Vanag, Chaos 15, 047510 (2005).
43. L. Stenflo and M. Y. Yu, Phys. Fluids B 1, 1543 (1989).
44. A. Kaminaga, V. K. Vanag, and I. R. Epstein, J. Chem. Phys. 122, 174706 (2005).
45. D. G. Míguez, S. Alonso, A. P. Muuzuri, and F. Sagús, Phys. Rev. Lett. 97, 178301 (2006).
46. D. Haim, G. Li, Q. Ouyang, W. D. McCormick, H. L. Swinney, A. Hagberg, and E. Meron, Phys. Rev. Lett. 77, 190 (1996).
47. C. B. Muratov, Phys. Rev. E 55, 1463 (1997).
48. I. Muller, E. Ammelt, and H. G. Purwins, Phys. Rev. Lett. 82, 3428 (1999).
49. K. J. Lee, W. D. McCormick, J. E. Pearson, and H. L. Swinney, Nature 369, 215 (1994).
50. K. J. Lee and H. L. Swinney, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 1149 (1997).
51. Y. A. Astrov and H. G. Purwins, Phys. Lett. A 358, 404 (2006).
52. V. K. Vanag, L. Yang, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, Nature 406, 389 (2000).
53. V. K. Vanag, A. M. Zhabotinsky, and I. R. Epstein, J. Phys. Chem. A 104, 11566 (2000).
54. V. K. Vanag, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. Lett. 86, 552 (2001).
55. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, Faraday Discuss. 120, 383 (2001).
56. T. Sakurai, E. Mihaliuk, F. Chirila, and K. Showalter, Science 296, 2009 (2002).
57. H. H. Rotermund, S. Jakubith, A. von Oertzen, and G. Ertl, Phys. Rev. Lett. 66, 3083 (1991).
58. Y. A. Astrov and H. G. Purwins, Phys. Lett. A 283, 349 (2001).
59. V. I. Zarnitsina, F. I. Ataullakhanov, A. I. Lobanov, and O. L. Morozova, Chaos 11, 57 (2001).
60. P. Coullet, C. Riera, and C. Tresser, Phys. Rev. Lett. 84, 3069 (2000).
61. A. Doelman, R. A. Gardner, and T. J. Kaper, Physica D 122, 1 (1998).
62. O. Jensen, V. O. Pannbacker, G. Dewel, and P. Borckmans, Phys. Lett. A 179, 91 (1993).
63. O. Jensen, V. O. Pannbacker, E. Mosekilde, G. Dewel, and P. Borckmans, Phys. Rev. E 50, 736 (1994).
64. R. E. Goldstein, D. J. Muraki, and D. M. Petrich, Phys. Rev. E 53, 3933 (1996).
65. A. Ito and T. Ohta, Phys. Rev. A 45, 8374 (1992).
66. T. Kolokolnikov, T. Erneux, and J. Wei, Physica D 214, 63 (2006).
67. C. B. Muratov and V. V. Osipov, J. Phys. A 33, 8893 (2000).
68. C. B. Muratov, Phys. Rev. E 66, 066108 (2002).
69. T. Ohta, M. Mimura, and R. Kobayashi, Physica D 34, 115 (1989).
70. B. S. Kerner and V. V. Osipov, Sov. Phys. JETP 47, 874 (1978).
71. C. B. Muratov and V. V. Osipov, SIAM J. Appl. Math. 62, 1463 (2002).
72. V. V. Osipov, Phys. Rev. E 48, 88 (1993).
73. H. Ikeda, M. Mimura, and Y. Nishiura, Nonlinear Anal. Theory, Methods Appl. 13, 507 (1989).
74. A. Yadav and D. A. Browne, Physica D 219, 142 (2006).
75. L. N. Bulaevskii and V. L. Ginzburg, Sov. Phys. JETP 18, 530 (1964).
76. P. Coullet, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, 2445 (2002).
77. L. Kramer, G. Gottwald, V. I. Krinsky, A. Pumir, and V. V. Barelko, Chaos 10, 731 (2000).
78. J.-A. Sepulchre and V. I. Krinsky, Chaos 10, 826 (2000).
79. B. S. Kerner and V. V. Osipov, Sov. Phys. JETP 52, 1122 (1980).
80. K. Krischer and A. Mikhailov, Phys. Rev. Lett. 73, 3165 (1994).
81. T. Ohta, Physica D 151, 61 (2001).
82. L. M. Pismen, J. Chem. Phys. 101, 3135 (1994).
83. D. M. Petrich and R. E. Goldstein, Phys. Rev. Lett. 72, 1120 (1994).
84. V. V. Osipov and A. V. Severtsev, Phys. Lett. A 227, 61 (1997).
85. P. Schutz, M. Bode, and V. V. Gafiichuk, Phys. Rev. E 52, 4465 (1995).
86. C. B. Muratov, Phys. Rev. E 54, 3369 (1996).
87. W. N. Reynolds, J. E. Pearson, and S. Ponce-Dawson, Phys. Rev. Lett. 72, 2797 (1994).
88. W. N. Reynolds, S. Ponce-Dawson, and J. E. Pearson, Phys. Rev. E 56, 185 (1997).
89. E. S. Lobanova and F. I. Ataullakhanov, Phys. Rev. Lett. 91, 138301 (2003).
90. D. Gomila, M. A. Matias, and P. Colet, Phys. Rev. Lett. 94, 063905 (2005).
91. D. Gomila, A. Jacobo, M. A. Matias, and P. Colet, Phys. Rev. E 75, 026217 (2007).
92. L. F. Yang, A. M. Zhabotinsky, and I. R. Epstein, Phys. Chem. Chem. Phys. 8, 4647 (2006).
93. O. Descalzi, Y. Hayase, and H. R. Brand, Phys. Rev. E 69, 026121 (2004).
94. B. Ermentrout, X. Chen, and Z. Chen, Physica D 108, 147 (1997).
95. H. Meinhardt and A. Gierer, J. Theor. Biol. 85, 429 (1980).
96. S. E. Folias and P. C. Bressloff, Phys. Rev. Lett. 95, 208107 (2005).
97. S. E. Folias and P. C. Bressloff, SIAM J. Appl. Math. 65, 2067 (2005).
98. S. V. Gurevich, S. Amiranashvili, and H. G. Purwins, Phys. Rev. E 74, 066201 (2006).
99. Y. Nishiura and M. Mimura, SIAM J. Appl. Math. 49, 481 (1989).
100. A. Hagberg and E. Meron, Nonlinearity 7, 805 (1994).
101. M. Suzuki, T. Ohta, M. Mimura, and H. Sakaguchi, Phys. Rev. E 52, 3645 (1995).
102. O. Descalzi and H. R. Brand, Phys. Rev. E 72, 055202 (2005).
103. C. B. Muratov and V. V. Osipov, Phys. Rev. E 54, 4860 (1996).
104. A. N. Zaikin, J. Physical Thought of Russia 1, 54 (1995).
105. S. V. Gurevich, H. U. Bodeker, A. S. Moskalenko, A. W. Liehr, and H. G. Purwins, Physica D 199, 115 (2004).
106. A. W. Liehr, H. U. Bodeker, M. C. Rottger, T. D. Frank, R. Friedrich, and H. G. Purwins, New J. Phys. 5, 89 (2003).
107. A. W. Liehr, A. S. Moskalenko, Y. A. Astrov, M. Bode, and H. G. Purwins, Eur. Phys. J. B 37, 199 (2004).
108. M. Bode, A. W. Liehr, C. P. Schenk, and H.-G. Purwins, Physica D 161, 45 (2002).
109. C. P. Schenk, M. Or-Guil, M. Bode, and H.-G. Purwins, Phys. Rev. Lett. 78, 3781 (1997).
110. E. R. Berlekamp, J. H. Conway, and R. L. Guy, Winning Ways for Your Mathematical Plays (Academic, London, 1982), Vol. 2.
111. A. Adamatzky, A. Wuensche, and B. D. Costello, Chaos, Solitons Fractals 27, 287 (2006).
112. L. Yang, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. E 62, 6414 (2000).
113. H. G. Rotstein, N. Kopell, A. M. Zhabotinsky, and I. R. Epstein, J. Chem. Phys. 119, 8824 (2003).
114. H. G. Rotstein, N. Kopell, A. M. Zhabotinsky, and I. R. Epstein, SIAM J. Appl. Math. 63, 1998 (2003).
115. H. G. Rotstein, A. A. Zhabotinsky, and I. R. Epstein, Phys. Rev. E 74, 016612 (2006).
116. H. G. Rotstein and R. Kuske, Physica D 215, 46 (2006).
117. C. P. Schenk, P. Schutz, M. Bode, and H. G. Purwins, Phys. Rev. E 57, 6480 (1998).
118. K. J. Lee, W. D. McCormick, Q. Ouyang, and H. L. Swinney, Science 261, 192 (1993).
119. K. J. Lee and H. L. Swinney, Phys. Rev. E 51, 1899 (1995).
120. J. E. Pearson, Science 261, 189 (1993).
121. I. Berenstein, Ph.D. thesis, Brandeis University (2005).