Inwardly rotating spiral wave breakup in oscillatory reaction-diffusion media

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 2, 2006, Pages

  Xie, Fagen ^a   Xie, Dongzhu ^b   Weiss, James N ^c  

^a Research Department   (United States)

^b SHANGHAI NORMAL UNIVERSITY   (China)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFUSION; NONLINEAR SYSTEMS;

DIFFUSION COEFFICIENT RATIO; HOPF BIFURCATION POINT; OSCILLATOR SYSTEM; OSCILLATORY REACTION-DIFFUSION SYSTEM;

OSCILLATORS (MECHANICAL);

EID: 33746918774     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.026107     Document Type: Article

References (26)

1. A. T. Winfree, When Time Breaks Down (Princeton University Press, Princeton, 1987);
2. Chemical Waves and Patterns, edited by, R. Kapral, and, K. Showalter, (Kluwer, Dordrecht, 1995);
3. J. Murray, Mathematical Biology (Springer, Berlin, 1989).
4. V. K. Vanag and I. R. Epstein, Science SCIEAS 0036-8075 10.1126/science.1064167 294, 835 (2001).
5. V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.228301 87, 228301 (2001);
6. V. K. Vanag and I. R. Epstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.088303 88, 088303 (2002).
7. Y. F. Gong and D. J. Christini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.088302 90, 088302 (2003).
8. L. Brusch, E. M. Nicola, and M. Bär, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.089801 92, 089801 (2004).
9. E. M. Nicola, L. Brusch, and M. Bär (unpublished).
10. Q. Ouyang, H. L. Swinney, and G. Li, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.1047 84, 1047 (2000).
11. M. Bär, M. Hildebrand, M. Eiswirth, M. Falcke, H. Engel, and M. Neufeld, Chaos CHAOEH 1054-1500 10.1063/1.166028 4, 499 (1994).
12. S. M. Tobias and E. Knobloch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.4811 80, 4811 (1998).
13. M. Bär and M. Or-Guil, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1160 82, 1160 (1999).
14. B. Sandstede and A. Scheel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.7708 62, 7708 (2000).
15. I. S. Aranson, L. Aranson, L. Kramer, and A. Weber, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.R2992 46, R2992 (1992).
16. M. Ipsen, L. Kramer, and P. G. Sorensen, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00062-4 337, 193 (2000).
17. I. S. Aranson and K. Kramer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.99 74, 99 (2002).
18. Q. Ouyang and J. M. Flesselles, Nature (London) NATUAS 0028-0836 10.1038/379143a0 379, 143 (1996).
19. F. H. Fenton and E. M. Cherry, Chaos CHAOEH 1054-1500 10.1063/1.1504242 12, 852 (2002).
20. J. N. Weiss, H. S. Karagueuzian, Z. L. Qu, and P. S. Chen, Circulation CIRCAZ 0009-7322 99, 2819 (1999).
21. R. A. FitzHugh, Biophys. J. BIOJAU 0006-3495 1, 445 (1961).
22. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B PTRBAE 0962-8436 237, 37 (1952).
23. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993), and references therein.
24. See EPAPS Document No. E-PLEEE8-74-066608 for computer simulation movies. For more information on EPAPS see http://www.aip.org/pubservs/epaps.html.
25. Chemical Oscillations, Waves, and Turbulence, edited by, Y. Kuramoto, (Springer-Verlag, Berlin, 1984).
26. P. S. Hagan. SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0142054 42, 762 (1982).