Model for line defects in complex-oscillatory spiral waves

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

Volumn 72, Issue 4, 2005, Pages

  Zhan, Meng ^a   Kapral, Raymond ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ARCHIMEDEAN SPIRAL SPLAY FIELD; POSSESS LINE DEFECTS; SPACE ORBITS; SPIRAL WAVES;

OSCILLATIONS; PHASE SPACE METHODS; TIME VARYING SYSTEMS;

ELECTROMAGNETIC WAVES;

EID: 28844476724     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.046221     Document Type: Article

References (30)

1. M. Cross and P. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993).
2. R. Kapral and K. Showalter, Chemical Waves and Patterns (Kluwer, Dordrecht, 1995).
3. I. S. Aranson and L. Kramer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.99 74, 99 (2002).
4. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin, 1984).
5. A. N. Zaikin and A. M. Zhabotinsky, Nature (London) NATUAS 0028-0836 10.1038/225535b0 225, 535 (1970).
6. A. T. Winfree, Science SCIEAS 0036-8075 175, 634 (1972).
7. G. Ertl, Adv. Catal. ADCAAX 0065-2342 37, 213 (1990).
8. A. Goldbeter, Biochemical Oscillations and Cellular Rhythms (Cambridge University Press, Cambridge, 1996).
9. A. T. Winfree, When Time Breaks Down (Princeton University Press, Princeton, 1987).
10. A. Goryachev and R. Kapral, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1619 76, 1619 (1996).
11. A. Goryachev and R. Kapral, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.5469 54, 5469 (1996).
12. A. Goryachev, H. Chate, and R. Kapral, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.873 80, 873 (1998)
13. A. Goryachev, H. Chate, and R. Kapral, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S021812749900170X 9, 2243 (1999).
14. J. Davidsen, R. Erichsen, R. Kapral, and H. Chate, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.018305 93, 018305 (2004).
15. J. S. Park and K. J. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.5393 83, 5393 (1999).
16. J. S. Park and K. J. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.224501 88, 224501 (2002).
17. J. S. Park, S. J. Woo, and K. J. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.098302 93, 098302 (2004).
18. H. Guo, L. Li, H. Wang, and Q. Ouyang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.056203 69, 056203 (2004).
19. K. D. Willamowski and O. E. Rössler, Z. Naturforsch. A ZENAAU 0044-3166 35, 317 (1980).
20. The simulations were performed using the explicit Euler method on a 256×256 square domain with no-flux boundary conditions. The diffusion coefficient was taken to be D=0.2. The space and time steps were Δx=1.0 and Δt=0.001. To achieve a perfect WR spiral wave, a special initial condition was used: D=0.067,Δt=0.01, and k2=1.480 were chosen with two lines of inhomogeneities to induce a rough spiral wave, followed by D=0.2 and Δt=0.001 for larger k2 to produce clean spirals.
21. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.4193 78, 4193 (1997).
22. A. L. Belmonte, Q. Ouyang, and J. M. Flesselles, J. Phys. II JPAHER 1155-4312 10.1051/jp2:1997195 7, 1425 (1997).
23. S. C. Muller, T. Plesser, and B. Hess, Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90068-6 24, 87 (1987).
24. K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.1749 65, 1749 (1990)
25. S. Nichols and K. Wiesenfeld, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.205 50, 205 (1994).
26. G. Hu, F. G Xie, Z. L. Qu, and P. L. Shi, Commun. Theor. Phys. CTPHDI 0253-6102 31, 99 (1999).
27. M. Zhan, G. Hu, Y. Zhang, and D. He, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1510 86, 1510 (2001).
28. T. Bohr, G. Huber, and E. Ott, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1996-00383-8 33, 589 (1996)
29. T. Bohr, G. Huber, and E. Ott Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00025-0 106, 95 (1997).
30. B. Sandstede and A. Scheel, SIAM J. Appl. Dyn. Syst. 1536-0040, 3, 1 (2004).