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The interaction between two spiral waves in two-layer excitable medium coupled indirectly through a passive medium and with time-delayed coupling is investigated by using the Bär model. The numerical results show that time-delayed coupling can either facilitate the synchronization of two spiral waves or lead to the transition from spiral wave to collective oscillation, different target waves, spatiotemporal chaos or rest state. Period-2 and period-3 spiral waves and the meander or drift of spiral wave are observed in the coupled excitable medium. The physical mechanism underlying these phenomena is discussed.
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Keywords:
- spiral wave /
- passive medium /
- time-delayed coupling /
- synchronization
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[15] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
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[20] Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifurcation and Chaos 21 587
[21] Qian Y 2012 Chin. Phys. B 21 088201
[22] Gao J Z, Yang S X, Xie L L, Gao J H 2011 Chin. Phys. B 20 030505
[23] 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 54 1510]
[24] Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681
[25] Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈永淇, 唐国宁 2012 61 020502]
[26] Zhou Z W, Chen X J, Tian T T, Tang G N 2012 Acta Phys. Sin. 61 210506 (in Chinese) [周振玮, 陈醒基, 田涛涛, 唐国宁2012 61 210506]
[27] Chen X J, Tian T T, Zhou Z W, Hu Y B, Tang G N 2012 Acta Phys. Sin. 61 210509 (in Chinese) [陈醒基, 田涛涛, 周振玮, 胡一博, 唐国宁2012 61 210509]
[28] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[29] Wang Q Y, Lu Q S 2005 Chin. Phys. Lett. 22 543
[30] Josephson M E, Horowitz L N, Farshidi A 1978 Circulation 57 659
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[1] Antzelevitch C 2001 Cardiovasc. Res. 50 426
[2] Petrov V S, Osipov G V, Kurths J 2010 Phys. Rev. E 82 026208
[3] Kaneko T, Nomura F, Yasuda K 2011 J. Nanobiotechnol. 9 21
[4] Haraguchi Y, Shimizu T, Yamato M, Kikuchi A, Okano T 2006 Biomaterials 27 4765
[5] Kohl P, Camelliti P, Burton F L, Smith G L 2005 J. Electrocardiol. 38 45
[6] Sachse F B, Moreno A P, Abildskov J A 2008 Ann. Biomed. Eng. 36 41
[7] Yue L X, Xie J, Nattel S 2011 Cardiovasc. Res. 89 744
[8] Miragoli M, Salvarini N, Rohr S 2007 Circ. Res. 101 755
[9] Shamim W, Francis D P, Yousufuddin M, Varney S, Pieopli M F, Anker S D, Coats A J S 1999 Int. J. Cardiol. 70 171
[10] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[11] Kanter R J, Pfeiffer R, Hu D, Barajas-Martinez H, Carboni M P, Antzelevitch C 2012 Circulation 125 14
[12] Biktashev V N, Holden A V 1998 Chaos 8 48
[13] Deng M Y, Tang G N, Kong L J, Liu M R 2010 Acta Phys. Sin. 59 2339 (in Chinese) [邓敏艺, 唐国宁, 孔令江, 刘慕仁 2010 59 2339]
[14] Li G Z, Chen Y Q, Tang G N, Liu J X 2011 Chin. Phys. Lett. 28 020504
[15] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[16] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[17] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[18] Qian Y, Song X Y, Shi W, Chen G Z, Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱郁, 宋宣玉, 时伟, 陈光旨, 薛郁 2006 55 4420]
[19] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[20] Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifurcation and Chaos 21 587
[21] Qian Y 2012 Chin. Phys. B 21 088201
[22] Gao J Z, Yang S X, Xie L L, Gao J H 2011 Chin. Phys. B 20 030505
[23] 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 54 1510]
[24] Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681
[25] Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈永淇, 唐国宁 2012 61 020502]
[26] Zhou Z W, Chen X J, Tian T T, Tang G N 2012 Acta Phys. Sin. 61 210506 (in Chinese) [周振玮, 陈醒基, 田涛涛, 唐国宁2012 61 210506]
[27] Chen X J, Tian T T, Zhou Z W, Hu Y B, Tang G N 2012 Acta Phys. Sin. 61 210509 (in Chinese) [陈醒基, 田涛涛, 周振玮, 胡一博, 唐国宁2012 61 210509]
[28] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[29] Wang Q Y, Lu Q S 2005 Chin. Phys. Lett. 22 543
[30] Josephson M E, Horowitz L N, Farshidi A 1978 Circulation 57 659
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