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The dynamics of spiral waves in a two-layer coupled excitable medium is studied by using the Bär-Eiswirth model. The two layers of medium are connected via network, i.e., a excitable unit is selected in each column of an excitable medium as a central point, and all excitable units in the same column of a layer medium are connected only with the corresponding central point and its eight neighbors in the opposite medium. The numerical results show that when the coupling strength is appropriately small, the two coupled spiral waves via local coupling can achieve their synchronization. Increasing coupling strength will induce meandering and drifting of spiral waves, leading to a desynchrony between the coupled spiral waves. The spiral wave with the resting state, low frequency plan wave and irregular pattern are observed to coexist. The coupled spiral waves via the transformation of spiral wave to synchronous plane wave disappear if the coupling strength is appropriately chosen. The physical mechanisms behind these phenomena are discussed.
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Keywords:
- spiral wave /
- excitable medium /
- network coupling /
- synchronization
[1] Mller S C, Plesser T, Hess B 1985 Science New Series 230 661
[2] Belmonte A L, Ouyang Q, Flesselles J M 1997 J. Phys. II France 7 1425
[3] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[4] Pertsov A M, Davidenko J M, Salomonsz R, Baxter W T, Jalife J 1993 Circ. Res. 72 631
[5] Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science New Series 252 123
[6] Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978
[7] Qian Y 2012 Chin. Phys. B 21 088201
[8] Seipel M, Schneider F W, Mnster A F 2001 Faraday Discuss. 120 395
[9] Steinbock O, Zykov V, Mller S C 1993 Nature 366 322
[10] Ma J, Jin W Y, Yi M, Li Y L 2008 Acta Phys. Sin. 57 2832 (in Chinese) [马军, 靳伍银, 易鸣, 李延龙 2008 物理学报 57 2832]
[11] Qiu K, Tang J, Luo J M, Ma J 2013 Chin. Phys. Lett. 30 118701
[12] Zhou C S, Zemanová L, Zamora-Lopez G, Hilgetag C C, Kurths J 2007 New J. Phys. 9 178
[13] Clayton R H, Bernus O, Cherry E M, Dierckx H, Fenton F H, Mirabella L, Panfilov A V, Sachse F B, Seemann G, Zhang H 2011 Prog. Biophys. Molecul. Biol. 104 22
[14] Gaudesius G, Miragoli M, Thomas S P, Rohr S 2003 Circ. Res. 93 421
[15] He D H, Hu G, Zhan M, Ren W, Gao Z 2002 Phys. Rev. E 65 055204
[16] Wang X N, Lu Y, Jiang M X, Ouyang Q 2004 Phys. Rev. E 69 056223
[17] Hooks D A, Trew M L, Caldwell B J, Sands G B, LeGrice I J, Smaill B H 2007 Circ. Res. 101 e103
[18] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[19] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[20] 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 物理学报 61 020502]
[21] Chen X J, Qiao C G, Wang L L, Zhou Z W, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 128201 (in Chinese) [陈醒基, 乔成功, 王利利, 周振玮, 田涛涛, 唐国宁 2013 物理学报 62 128201]
[22] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[23] Zhang H, Wu N J, Ying H P, Hu G, Hu B 2004 J. Chem. Phys. 121 7276
[24] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[25] Liu G Q, Ying H P 2014 Chin. Phys. B 23 050502
[26] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[27] Ishida H, Genka C, Hirota Y, Nakazawa H, Barry W H 1999 Biophys. J. 77 2114
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[1] Mller S C, Plesser T, Hess B 1985 Science New Series 230 661
[2] Belmonte A L, Ouyang Q, Flesselles J M 1997 J. Phys. II France 7 1425
[3] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[4] Pertsov A M, Davidenko J M, Salomonsz R, Baxter W T, Jalife J 1993 Circ. Res. 72 631
[5] Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science New Series 252 123
[6] Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978
[7] Qian Y 2012 Chin. Phys. B 21 088201
[8] Seipel M, Schneider F W, Mnster A F 2001 Faraday Discuss. 120 395
[9] Steinbock O, Zykov V, Mller S C 1993 Nature 366 322
[10] Ma J, Jin W Y, Yi M, Li Y L 2008 Acta Phys. Sin. 57 2832 (in Chinese) [马军, 靳伍银, 易鸣, 李延龙 2008 物理学报 57 2832]
[11] Qiu K, Tang J, Luo J M, Ma J 2013 Chin. Phys. Lett. 30 118701
[12] Zhou C S, Zemanová L, Zamora-Lopez G, Hilgetag C C, Kurths J 2007 New J. Phys. 9 178
[13] Clayton R H, Bernus O, Cherry E M, Dierckx H, Fenton F H, Mirabella L, Panfilov A V, Sachse F B, Seemann G, Zhang H 2011 Prog. Biophys. Molecul. Biol. 104 22
[14] Gaudesius G, Miragoli M, Thomas S P, Rohr S 2003 Circ. Res. 93 421
[15] He D H, Hu G, Zhan M, Ren W, Gao Z 2002 Phys. Rev. E 65 055204
[16] Wang X N, Lu Y, Jiang M X, Ouyang Q 2004 Phys. Rev. E 69 056223
[17] Hooks D A, Trew M L, Caldwell B J, Sands G B, LeGrice I J, Smaill B H 2007 Circ. Res. 101 e103
[18] Nie H C, Xie L L, Gao J H, Zhan M 2011 Chaos 21 023107
[19] Hildebrand M, Cui J X, Mihaliuk E, Wang J C, Showalter K 2003 Phys. Rev. E 68 026205
[20] 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 物理学报 61 020502]
[21] Chen X J, Qiao C G, Wang L L, Zhou Z W, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 128201 (in Chinese) [陈醒基, 乔成功, 王利利, 周振玮, 田涛涛, 唐国宁 2013 物理学报 62 128201]
[22] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[23] Zhang H, Wu N J, Ying H P, Hu G, Hu B 2004 J. Chem. Phys. 121 7276
[24] Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[25] Liu G Q, Ying H P 2014 Chin. Phys. B 23 050502
[26] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[27] Ishida H, Genka C, Hirota Y, Nakazawa H, Barry W H 1999 Biophys. J. 77 2114
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