Bifurcation and stability analysis of rotating chemical spirals in circular domains: Boundary-induced meandering and stabilization

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

Volumn 67, Issue 5 2, 2003, Pages

  Bär, Markus ^a   Bangia, Anil K ^b   Kevrekidis, Ioannis G ^b  

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

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; INTEGRATION; MICROSTRUCTURE; NUMERICAL ANALYSIS; ORDINARY DIFFERENTIAL EQUATIONS; PLATINUM; STABILITY; SURFACES;

BOUNDARY INDUCED MEANDERING; ROTATING CHEMICAL SPIRALS; STABILITY ANALYSIS;

CHEMICAL REACTIONS;

EID: 42749108525     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. V.S. Zykov, Biophysics (Engl. Transl.) 31, 862 (1986).
2. A.T. Winfree, Chaos 1, 303 (1991).
3. A.S. Mikhailov and V.S. Zykov, Physica D 52, 379 (1991).
4. A. Karma, Chaos 4, 461 (1994).
5. J.P. Keener and J.J. Tyson, Physica D 21, 300 (1986).
6. D.A. Kessler and H. Levine, Physica D 49, 90 (1991).
7. D. Barkley, Phys. Rev. Lett. 68, 2090 (1992).
8. S.C. Müller, T. Plesser, and B. Hess, Science 230, 661 (1985).
9. G.S. Skinner, and H.L. Swinney, Physica D 48, 1 (1990).
10. S. Nettesheim, A. von Oertzen, H.H. Rotermund, and G. Ertl, J. Chem. Phys. 98, 9977 (1993).
11. S. Rica and E. Tirapegui, Phys. Rev. Lett. 64, 878 (1990).
12. C. Elphick and E. Meron, Physica D 53, 385 (1991).
13. I.S. Aranson, L. Kramer, and A. Weber, Phys. Rev. E 47, 3231 (1993).
14. V.A. Davydov and V.S. Zykov, Zh. Eksp. Teor. Fiz. 76, 414 (1993).
15. I.S. Aranson, D. Kessler, and I. Mitkov, Phys. Rev. E 50, R2395 (1994).
16. A. K. Bangia, Ph.D. thesis, Princeton University, 1997.
17. N. Hartmann, M. Bär, I.G. Kevrekidis, K. Krischer, and R. Imbihl, Phys. Rev. Lett. 76, 1384 (1996).
18. N. Hartmann, I.G. Kevrekidis, and R. Imbihl, J. Chem. Phys. 112, 6795 (2000).
19. P.C. Fife, J. Stat. Phys. 39, 687 (1985).
20. A. Bernoff, Physica D 53, 125 (1991).
21. P. Pelcé and J. Sun, Physica D 48, 353 (1991).
22. P. Pelcé and J. Sun, Physica D 63, 273 (1993).
23. A. Karma, Phys. Rev. Lett. 68, 397 (1992).
24. D. Kessler and R. Kupferman, Physica D 97, 509 (1996).
25. D. Margerit and D. Barkley, Phys. Rev. Lett. 86, 175 (2001).
26. N. Wiener and A. Rosenblueth, Arch. Inst. Cardiol. Mex. 16, 205 (1946).
27. V. S. Zykov, Simulation of Wave Processes in Excitable Media (Manchester University Press, New York, 1987).
28. D. Barkley, Physica D 49, 61 (1991).
29. A. Karma, Phys. Rev. Lett. 65, 2824 (1990).
30. A.M. Pertsov, A.V. Panfilov, and E.A. Ermakova, Physica D 14, 117 (1984).
31. M. Bär and M. Eiswirth, Phys. Rev. E 48, R1635 (1993).
32. M. Bär, N. Gottschalk, M. Eiswirth, and G. Ertl, J. Chem. Phys. 100, 1202 (1994).
33. D. Barkley, in Chemical Waves a D. Barkley, in Chemical Waves ater and R. Kapral (Kluwer, Dordrecht, 1995).
34. D. Barkley, Phys. Rev. Lett. 72, 164 (1994).
35. J.R. Leis and M.A. Kramer, ACM Trans. Math. Softw. 14, 61 (1988).
36. Y. Saad, Numerical Methods for Large Eigenvalue Problems (Manchester University Press, Manchester, 1992).
37. I. Goldhirsch, S.A. Orszag, and B.K. Maulik, J. Sci. Comput. 2, 33 (1987).
38. K.N. Christodoulou and L.E. Scriven, J. Sci. Comput. 3, 355 (1988).
39. Y. Saad and M.H. Schultz, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856 (1986).
40. K. Agladze, J.P. Keener, S.C. Müller, and A. Panfilov, Science 264, 1746 (1994).
41. J.A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 187 (1993).
42. S. C. Müller and V. S. Zykov, in Dynamical Phenomena in Living Cells, edited by E. Moseskilde and O. G. Mouritsen (Springer, Berlin, 1995).
43. M. Gomez-Gesteira, A.P. Munuzuri, V. Perez-Munuzuri, and V. Perez-Villar, Phys. Rev. E 53, 5480 (1996).
44. H. Brandstädter, M. Braune, I. Schebesch, and H. Engel, Chem. Phys. Lett. 323, 145 (2000).
45. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, Phys. Rev. E 65, 065602 (2002).