Unified approach to feedback-mediated control of spiral waves in excitable media

Analysis And Control Of Complex Nonlinear Processes In Physics, Chemistry And Biology

Volumn , Issue , 2007, Pages 243-272

  Zykov, Vladimir S ^a   Engel, Harald ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85043597235     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812706911_0009     Document Type: Chapter

References (55)

1. G. Gerisch, Naturwissenschaften 58, 430 (1971).
2. A.T. Winfree, Science 175, 634 (1972).
3. A.M. Zhabotinsky and A.N. Zaikin, J. Theor. Biol. 40, 45 (1973).
4. M.A. Allessie, F.I.M. Bonke, and F.J.G. Schopman, Circ. Res. 33, 54 (1973).
5. J.M. Davidenko, A.V. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Nature 355, 349 (1992).
6. N.A. Gorelova and J. Bures, J. Neurobiol. 14, 353 (1983).
7. S. Jakubith, H.H. Rotermund, W. Engel, A. von Oertzen, and G. Ertl, Phys. Rev. Lett. 65, 3013 (1990).
8. J. Lechleiter, S. Girard, E. Peralta, and D. Clapham, Science 252, 123 (1991).
9. T. Mair and S.C. Müller, J. Biol. Chem. 271, 627 (1996).
10. A. T. Winfree: The Geometry of Biological Time (Springer, Berlin, Heidelberg, 2000).
11. Y. Kuramoto: Chemical Oscillations, Waves and Turbulence (Springer, Berlin, Heidelberg, 1984).
12. V. Krinsky and H. Swinney (eds): Wave and patterns in biological and chemical excitable media (North-Holland, Amsterdam, 1991).
13. R. Kapral and K. Showalter (eds.): Chemical Waves and Patterns (Kluwer, Dordrecht, 1995).
14. V.A. Davydov, V.S. Zykov, and A.S. Mikhailov, Usp. Fiz. Nauk 161, 45 (1991) [Sov. Phys. Usp. 34, 665 (1991)].
15. R.M. Mantel and D. Barkley, Phys. Rev. E 54, 4791 (1996).
16. V. Hakim and A. Karma, Phys. Rev. E 60, 5073 (1999).
17. B. Sandstede, A. Scheel, and C. Wulff, J. Nonlin. Sei. 9, 439 (1999).
18. K.I. Agladze, V.A. Davydov, and A.S. Mikhailov, JETP Lett. 45, 767 (1987).
19. S. Grill, V.S. Zykov, and S.C. Müller, J. Phys. Chem. 100, 19082 (1996).
20. V.N. Biktashev and A. Holden, J. Theor. Biol. 169, 101 (1994).
21. S. Grill, V.S. Zykov, and S.C. Müller, Phys. Rev. Lett. 75, 3368 (1995).
22. Y.E. Volodin, V.V. Barelko, and A.G. Merzhanov, Sov. J. Chem. Phys. 5, 1146 (1982).
23. C. Radehaus, K. Kardell, H. Baumann, P. Jäger, and H.-G. Purwins, Z. Phys. B-Condensed Matter 65, 515 (1987).
24. S.L. Lane and D. Luss, Phys. Rev. Lett. 70, 830 (1993).
25. E. Schöll, Nonlinear spatio-temporal dynamics and chaos in semiconductors, (Cambridge Univ. Press, Cambridge, 2001).
26. V.K. Vanag, L. Yang, M. Dolnik, A.M. Zhabotinsky, and I. Epstein, Nature 406, 389 (2000).
27. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, Phys. Rev. E 65, 065602 (2002).
28. M. Kim, M. Bertram, M. Pollman, A. von Oertzen, A.S. Mikhailov, H.H. Rotermund, and G. Ertl, Science 292, 1357 (2001).
29. H. Brandtstädter, M. Braune, I. Schebesch, and H. Engel, Chem. Phys. Lett. 323, 145 (2000).
30. V.S. Zykov, G. Bordiougov, H. Brandtstädter, I. Gerdes, and H. Engel, Phys. Rev. E 68, 016214 (2003).
31. V.S. Zykov, G. Bordiougov, H. Brandtstädter, I. Gerdes, and H. Engel, Phys. Rev. Lett. 92, 18304 (2004).
32. H.-J. Krug, L. Pohlmann, and L. Kuhnert, J. Phys. Chem. 94, 4862 (1990).
33. N. Wiener and A. Rosenblueth, Arch.Inst. Cardiol. Mex. 16, 205 (1946).
34. V.S. Zykov, Simulation of Wave Processes in Excitable Media (Manchester Univ. Press, Manchester, 1987).
35. V.S. Zykov and O.L. Morozova, Biophysics 24, 739 (1980).
36. J.J. Tyson, and J.P. Keener, Physica D 32, 327 (1988).
37. J. Gomatam, and D.A. Hodson, Physica D 49, 82 (1991).
38. F.B. Gul’ko and A.A. Petrov, Biofizika 17, 261 (1972).
39. V.S. Zykov, Biophysics 25, 329 (1980).
40. A. Karma and V.S. Zykov, Phys. Rev. Lett. 83, 2453 (1999).
41. P.S. Hagan, SIAM J. Appl. Math. 42, 762 (1982).
42. I.S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
43. V.S. Zykov, O. Kheowan, O. Rangsiman, and S.C. Müller, Phys. Rev. E 65, 026206 (2002).
44. D. Barkley, M. Kness, and L.S. Tuckerman, Phys. Rev. A 42, 2489 (1990).
45. S. Nettesheim, A. von Oertzen, H.H. Rotermund, and G. Ertl, J. Chem. Phys. 98, 9977 (1993).
46. M. Braune and H. Engel, Phys. Rev. E 62, 5986 (2000).
47. V.S. Zykov and H. Engel, Physica D 199, 243 (2004).
48. O. Kheowan, C.K. Chan, V.S. Zykov, O. Rangsiman, and S.C. Müller, Phys. Rew. E 64, 035201(R), (2001).
49. O. Kheowan, V.S. Zykov, and S.C. Müller, Phys. Chem. Chem. Phys. 4, 1334 (2002).
50. V.S. Zykov and H. Engel, Phys. Rev. E 66, 16206 (2002).
51. V.S. Zykov, A.S. Mikhailov, and S.C. Müller, Phys. Rev. Lett., 78, 3398 (1997).
52. O. Kheowan and S.C. Müller, Appl. Math. Comput. 164, 373 (2005).
53. V.S. Zykov, H. Brandtstädter, G. Bordiougov, and H. Engel, Phys. Rev. E 72, 065201(R) (2005).
54. B. Fiedler and S. Liebscher, in: Proc. of the International Congress of Mathematicians, ICM 2002, Vol. III, Higer Education Press, Beijing, pp. 305-316 (2002).
55. B. Fiedler, M. Georgi, and N. Jangle, Chapter 3 in this volume.