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The dynamics of spiral wave in a three-layer excitable medium with circular feedback coupling is studied, based on the Bär model. The numerical results show that the drifting or meandering of spiral waves in the subsystems can be observed when the coupling strength is small. When the coupling strength is slightly big, the interaction between subsystems may cause spiral waves in some subsystems to move out of the boundaries of the subsystems. The subsystems return to rest state. In addition, the interaction may generate the transition from spiral wave state to target wave or turbulence states in some subsystems. The phenomenon that the asymptotic state of a subsystem depends on the initiation condition is observed. With the further increase of the coupling strength, the approximate generalized synchronization of the spiral waves in three subsystems is established. When the coupling strength is bigger, the spiral waves evolve into turbulence.
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Keywords:
- excitable medium /
- spiral wave /
- synchronization
[1] Zaikin A N, Zhabotinsky A M 1970 Nature(London) 225 535
[2] Bär M, Gottschalk N, Ertl G 1994 J. Phys. Chem. B 100 1202
[3] Gray R A, Pertsov A M, Jalife J 1998 Nature (London) 392 75
[4] Witkowski F X, Leon L J, Penkoske P A,Giles W R, Spano M L, Ditto W L,Winfree A T 1998 Nature (London) 392 78
[5] Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science 252 123
[6] Harris-White M E, Zanotti S A, Frautschy S A, Charles A C 1998 J. Neurophysiol 79 1045
[7] Wilkins M, Sneyd J 1998 J. Theor Biol 191 299
[8] Berenstein I, Mu?nuzuri A P , Yang L, Dolnik M, Zhabotinsky A M, Epstein I R 2008 Phys. Rev. E 78 025101(R)
[9] Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 唐国宁 2010 物理学报 59 2319]
[10] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 66 (in Chinese) [韦海明, 唐国宁 2011 物理学报 60 66]
[11] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[12] Yuan G Y, Yang S P, Wang G R, Chen S G 2005 Acta Phys. Sin. 54 1510 (in Chinese) [袁国勇, 杨世平, 王光瑞, 陈式刚 2005 物理学报 54 1510]
[13] Zhan M, Wang X G, Gong X F, Lai C H 2005 Phys. Rev. E 71 036212
[14] Zhou T S, Chen L N, Aihara K 2005 Phys. Rev. Lett. 95 178103
[15] Ma J, Ying H P, Liu Y, Li S R 2009 Chin. Phys. B 18 0098
[16] Zhang G Y, Ma J, Yu L C, Chen Y 2008 Chin. Phys. B 17 4107
[17] Resmi V, Ambika G 2010 Phys. Rev. E 81 046216
[18] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
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[1] Zaikin A N, Zhabotinsky A M 1970 Nature(London) 225 535
[2] Bär M, Gottschalk N, Ertl G 1994 J. Phys. Chem. B 100 1202
[3] Gray R A, Pertsov A M, Jalife J 1998 Nature (London) 392 75
[4] Witkowski F X, Leon L J, Penkoske P A,Giles W R, Spano M L, Ditto W L,Winfree A T 1998 Nature (London) 392 78
[5] Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science 252 123
[6] Harris-White M E, Zanotti S A, Frautschy S A, Charles A C 1998 J. Neurophysiol 79 1045
[7] Wilkins M, Sneyd J 1998 J. Theor Biol 191 299
[8] Berenstein I, Mu?nuzuri A P , Yang L, Dolnik M, Zhabotinsky A M, Epstein I R 2008 Phys. Rev. E 78 025101(R)
[9] Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 唐国宁 2010 物理学报 59 2319]
[10] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 66 (in Chinese) [韦海明, 唐国宁 2011 物理学报 60 66]
[11] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[12] Yuan G Y, Yang S P, Wang G R, Chen S G 2005 Acta Phys. Sin. 54 1510 (in Chinese) [袁国勇, 杨世平, 王光瑞, 陈式刚 2005 物理学报 54 1510]
[13] Zhan M, Wang X G, Gong X F, Lai C H 2005 Phys. Rev. E 71 036212
[14] Zhou T S, Chen L N, Aihara K 2005 Phys. Rev. Lett. 95 178103
[15] Ma J, Ying H P, Liu Y, Li S R 2009 Chin. Phys. B 18 0098
[16] Zhang G Y, Ma J, Yu L C, Chen Y 2008 Chin. Phys. B 17 4107
[17] Resmi V, Ambika G 2010 Phys. Rev. E 81 046216
[18] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
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