Pattern formation in excitable media with concentration-dependent diffusivities

Journal of Chemical Physics

Volumn 120, Issue 17, 2004, Pages 8079-8088

  Roussel, Marc R ^a   Wang, Jichang ^b  

^a UNIVERSITY OF LETHBRIDGE   (Canada)

^b UNIVERSITY OF WINDSOR   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442642800     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1689640     Document Type: Article

References (70)

1. G. Nicolis and P. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New York, 1977).
2. Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995).
3. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952).
4. K. Showalter, J. Chem. Phys. 73, 3735 (1980).
5. V. Castets, E. Dulos, J. Boissonade, and P. De Kepper, Phys. Rev. Lett. 64, 2953 (1990).
6. Q. Ouyang and H. L. Swinney, Nature (London) 352, 610 (1991).
7. I. Lengyel, S. Kádár, and I. R. Epstein, Science 259, 493 (1993).
8. J. D. Dockery and R. J. Field, Phys. Rev. E 58, 823 (1998).
9. P. Andresén, M. Bache, E. Mosekilde, G. Dewel, and P. Borckmanns, Phys, Rev. E 60, 297 (1999).
10. M. Kærn and M. Menzinger, Phys. Rev. E 60, 3471 (1999).
11. R. A. Satnoianu and M. Menzinger, Phys. Rev. E 62, 113 (2000).
12. M. R. Roussel and J. Wang, Phys. Rev. Lett. 87, 188302 (2001); 90, 119902(E) (2003).
13. M. R. Roussel and J. Wang, Phys. Rev. Lett. 87, 188302 (2001); 90, 119902(E) (2003).
14. S. Kádár, J. Wang, and K. Showalter, Nature (London) 391, 770 (1998).
15. I. Sendiña-Nadal, A. P. Muñuzuri, D. Vives, V. Pérez-Muñuzuri, J. Casademunt, L. Ramírez-Piscina, J. M. Sancho, and F. Sagués, Phys. Rev. Lett. 80, 5437 (1998).
16. C. J. Hemming and R. Kapral, Chaos 10, 720 (2000).
17. P. Jung and G. Mayer-Kress, Phys. Rev. Lett. 74, 2130 (1995).
18. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
19. M. Hendrey, E. Ott, and T. M. Antonsen, Jr., Phys. Rev. E 61, 4943 (2000).
20. W. Zimmermann, B. Painter, and R. Behringer, Eur. Phys. J. B 5, 757 (1998).
21. S. Bouzat and H. S. Wio, Phys. Lett. A 268, 323 (2000).
22. H. Malchow, J. Theor. Biol. 135, 371 (1988).
23. R. Larter and P. Ortoleva, J. Theor. Biol. 88, 599 (1981).
24. A. Okubo, Diffusion and Ecological Problems: Mathematical Models (Springer-Verlag, Berlin, 1979).
25. J. D. Murray, Mathematical Biology (Springer-Verlag, Berlin, 1989).
26. D. del-Castillo-Negrete, B. A. Carreras, and V. Lynch, Physica D 168-169, 45 (2002).
27. Z. Chvoj, H. Conrad, V. Cháb, M. Ondrejcek, and A. M. Bradshaw, Surf. Sci. 329, 121 (1995).
28. C. Uebing and R. Gomer, Ber. Bunsenges. Phys. Chem. 100, 1138 (1996).
29. Z. Wei, R. Verhoef, M. Asscher, I. Farbman, and A. Ben-Shaul, Appl. Surf. Sci. 106, 80 (1996).
30. E. D. Westre, D. E. Brown, J. Kutzner, and S. M. George, J. Chem. Phys. 104, 7313 (1996).
31. J. T. Goldstein and G. Ehrlich, Surf. Sci. 420, l (1999).
32. V. V. Gvozdev and Yu. K. Tovbin, Chem. Phys. Rep. 18, 179 (1999).
33. M. Tammaro and J. W. Evans, Surf. Sci. 395, L207 (1998).
34. M. Tammaro and J. W. Evans, Phys. Rev. E 57, 5087 (1998).
35. R. Yoshida, M. Tanaka, S. Onodera, T. Yamaguchi, and E. Kokufuta, J. Phys. Chem. A 104, 7549 (2000).
36. S. E. Kudaibergenov and V. B. Sigitov, Langmuir 15, 4230 (1999).
37. H. Malchow, Z. Phys. Chem. (Leipzig) 271, 751 (1990).
38. H. Malchow, H. Rosé, and C. Sattler, J. Non-Equilib. Thermodyn. 17, 41 (1992).
39. H. Malchow, Physica A 213, 159 (1995).
40. H. Malchow, Z. Phys. Chem. (Munich) 204, 95 (1998).
41. D. C. Spray, A. L. Harris, and M. V. L. Bennett, Science 211, 712 (1981).
42. F. Brümmer, G. Zempel, P. Bühle, J.-C. Stein, and D. F. Hülser, Exp. Cell Res. 196, 158 (1991).
43. A. Uehara, M. Yasukochi, and I. Imanaga, J. Mol. Cell. Cardiol. 26, 195 (1994).
44. H. Tributsch and L. Pohlmann, J. Theor. Biol. 178, 17 (1996).
45. D. Meredith and C. A. R. Boyd, Cell. Mol. Life Sci. 57, 754 (2000).
46. G. L. Kellert, J. Physiol. (London) 531, 585 (2001).
47. G. J. Mitchison, Proc. R. Soc. London, Ser. B 207, 79 (1980).
48. H. G. Othmer and E. Pate, Proc. Natl. Acad. Sci. U.S.A. 77, 4180 (1980).
49. E. Pate and H. G. Othmer, Differentiation (Berlin) 28, l (1984).
50. E. F. Pate and H. G. Othmer, J. Theor. Biol. 118, 301 (1986).
51. A. Hunding, J. Math. Biol. 25, 109 (1987).
52. A. Hunding and P. G. Sørensen, J. Math. Biol. 26, 27 (1988).
53. P. K. Maini, D. L. Benson, and J. A. Sherratt, IMA J. Math. Appl. Med. Biol. 9, 197 (1992).
54. P. K. Maini, J. Biol. Syst. 3, 987 (1995).
55. C. J. Roussel and M. R. Roussel, Prog. Biophys. Mol. Biol. (in press).
56. Y. Huang and O. Diekmann, Bull. Math. Biol. 65, 143 (2003).
57. P. Gray and S. K. Scott, Chem. Eng. Sci. 39, 1087 (1984).
58. J. H. Merkin, V. Petrov, S. K. Scott, and K. Showalter, Phys. Rev. Lett. 76, 546 (1996).
59. M. R. Roussel and J. Wang, Phys. Chem. Chem. Phys. 4, 1310 (2002); 4, 3152(E) 2002).
60. M. R. Roussel and J. Wang, Phys. Chem. Chem. Phys. 4, 1310 (2002); 4, 3152(E) 2002).
61. J. E. Pearson, Science 261, 189 (1993).
62. K. J. Lee, W. D. McCormick, Q. Ouyang, and H. L. Swinney, Science 261, 192 (1993).
63. W. N. Reynolds, J. E. Pearson, and S. Ponce-Dawson, Phys. Rev. Lett. 72, 2797 (1994).
64. A. Doelman, T. J. Kaper, and P. A. Zegeling, Nonlinearity 10, 523 (1997).
65. J. K. Hale, L. A. Peletier, and W. C. Troy, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 61, 102 (2000).
66. W. N. Reynolds, S. Ponce-Dawson, and J. E. Pearson, Phys. Rev. E 56, 185 (1997).
67. L. G. Harrison, Int. J. Plant Sci. 153, S76 (1992).
68. A. J. Koch and H. Meinhardt, Rev. Mod. Phys. 66, 1481 (1994).
69. W. E. Milne, Numerical Solution of Differential Equations, 2nd ed. (Dover, New York, 1970), Chap. 8.
70. C. F. Gerald, Applied Numerical Analysis, 2nd ed. (Addison-Wesley, Reading, MA, 1978), Sec. 7.9.