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The control of spiral waves in three-layer coupled excitable media is studied by using the Bär model. The bidirectional coupling between adjacent layers is adopted. We use planar waves generated by a local periodic signal added to the second layer to eliminate spiral waves in the media. The numerical results show that when the couplings among three layer media meet some conditions the spiral waves in the media can be controlled. The control of spiral waves may be achieved by using the complementary coupling strategy. The interaction between planar wave and low-frequency spiral wave can produce high-frequency spiral wave, leading to failure to eliminate spiral waves. There exists an optimal drive width. Both larger and smaller drive width may need larger coupling strength between the first and third layers. The control results depending on the control opportunity are observed. We hope that this study will contribute to the design of the implantable cardioverter defibrillator.
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Keywords:
- spiral wave /
- coupling /
- heart tissue /
- control
[1] Witkowski F X, Joshua L L, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78
[2] Gray R A, Jalife J, Panfilov A V, Baxter W T, Cabo C, Davidenko J M, Pertsov A M 1995 Science 270 1222
[3] Yuan G Y, Xu L, Xu A G, Wang G R, Yang S P 2011 Chaos, Solitons and Fractals 44 728
[4] Hendrey M, Ott E, Antonsen Jr T M 2000 Phys. Rev. E 61 4943
[5] Wang C N, Yang L J, Yuan L H, Ma J 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3913
[6] Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifurc. Chaos 21 587
[7] Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681
[8] Yuan G Y, Wang G R, Chen S G 2005 Commun. Theor. Phys. 44 858
[9] Cao Z J, Li P F, Zhang H, Xie F G, Hu G 2007 Chaos 17 015107
[10] de la Casa M A, de la Rubia F J, Ivanov P C 2007 Chaos 17 015109
[11] Cao Z J, Zhang H, Xie F G, Hu G 2006 Europhys. Lett. 75 875
[12] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟敏, 唐国宁 2010 59 3070]
[13] Ma J, Jia Y, Yi M, Tang J, Xia Y F 2009 Chaos, Solitons and Fractals 41 1331
[14] Sakaguchi H, Fujimoto T 2003 Phys. Rev. E 67 067202
[15] Zykov V S, Mikhailov A S, Müller S C 1997 Phys. Rev. Lett. 78 3398
[16] 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]
[17] Gray R A , Chattipakorn N 2005 Proc. Natl. Acad. Sci. U.S.A. 102 4672
[18] Gao J Z, Xie L L, Xie W M, Gao J H 2011 Acta Phys. Sin. 60 080503 (in Chinese) [高加振, 谢玲玲, 谢伟苗, 高继华 2011 60 080503]
[19] Piller L W 1970 Electronic Instrumentation Theory of Cardiac Technology (London: Staples Press)
[20] Walker R G, Koster R W, Sun C, Moffat G, Barger J, Dodson P P, Chapman F W 2009 Resuscitation 80 773
[21] Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931
[22] Allessie M, Kirchhof C, Scheffer G J, Chorro F, Brugada J 1991 Circulation 84 1689
[23] Yu C G, Bai R, Chen D L, Huang Y 2008 Cardiac Electrophysiology Basic and Clinical (WuHan: Huazhong University of Science and Technology Press) p4 (in Chinese) [余承高, 白融, 陈栋梁, 黄勇 2008 心脏电生理学基础与临床 (武汉: 华中科技大学出版社) 第4页]
[24] Antzelevitch C 2001 Cardiovascular Research 50 426
[25] Wang J M, Xue Y 2011 International Conference on Network Computing and Information Security Guilin, China, May 14-15, 2011 pp49-53
[26] 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]
[27] Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈咏琪, 唐国宁 2012 61 020502]
[28] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[29] Li X C, Wu X Y, Zhang S, Zhou Z H, Li L, Liang Z G, Li W M 2008 Chinese Journal of Cardiac Pacing and Electrophysiology 22 347 (in Chinese) [李秀春, 吴晓羽, 张姝, 周中华, 李磊, 梁兆光, 李为民 2008 中国心脏起搏与心电生理杂志 22 347]
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[1] Witkowski F X, Joshua L L, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78
[2] Gray R A, Jalife J, Panfilov A V, Baxter W T, Cabo C, Davidenko J M, Pertsov A M 1995 Science 270 1222
[3] Yuan G Y, Xu L, Xu A G, Wang G R, Yang S P 2011 Chaos, Solitons and Fractals 44 728
[4] Hendrey M, Ott E, Antonsen Jr T M 2000 Phys. Rev. E 61 4943
[5] Wang C N, Yang L J, Yuan L H, Ma J 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3913
[6] Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifurc. Chaos 21 587
[7] Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681
[8] Yuan G Y, Wang G R, Chen S G 2005 Commun. Theor. Phys. 44 858
[9] Cao Z J, Li P F, Zhang H, Xie F G, Hu G 2007 Chaos 17 015107
[10] de la Casa M A, de la Rubia F J, Ivanov P C 2007 Chaos 17 015109
[11] Cao Z J, Zhang H, Xie F G, Hu G 2006 Europhys. Lett. 75 875
[12] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟敏, 唐国宁 2010 59 3070]
[13] Ma J, Jia Y, Yi M, Tang J, Xia Y F 2009 Chaos, Solitons and Fractals 41 1331
[14] Sakaguchi H, Fujimoto T 2003 Phys. Rev. E 67 067202
[15] Zykov V S, Mikhailov A S, Müller S C 1997 Phys. Rev. Lett. 78 3398
[16] 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]
[17] Gray R A , Chattipakorn N 2005 Proc. Natl. Acad. Sci. U.S.A. 102 4672
[18] Gao J Z, Xie L L, Xie W M, Gao J H 2011 Acta Phys. Sin. 60 080503 (in Chinese) [高加振, 谢玲玲, 谢伟苗, 高继华 2011 60 080503]
[19] Piller L W 1970 Electronic Instrumentation Theory of Cardiac Technology (London: Staples Press)
[20] Walker R G, Koster R W, Sun C, Moffat G, Barger J, Dodson P P, Chapman F W 2009 Resuscitation 80 773
[21] Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931
[22] Allessie M, Kirchhof C, Scheffer G J, Chorro F, Brugada J 1991 Circulation 84 1689
[23] Yu C G, Bai R, Chen D L, Huang Y 2008 Cardiac Electrophysiology Basic and Clinical (WuHan: Huazhong University of Science and Technology Press) p4 (in Chinese) [余承高, 白融, 陈栋梁, 黄勇 2008 心脏电生理学基础与临床 (武汉: 华中科技大学出版社) 第4页]
[24] Antzelevitch C 2001 Cardiovascular Research 50 426
[25] Wang J M, Xue Y 2011 International Conference on Network Computing and Information Security Guilin, China, May 14-15, 2011 pp49-53
[26] 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]
[27] Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈咏琪, 唐国宁 2012 61 020502]
[28] Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[29] Li X C, Wu X Y, Zhang S, Zhou Z H, Li L, Liang Z G, Li W M 2008 Chinese Journal of Cardiac Pacing and Electrophysiology 22 347 (in Chinese) [李秀春, 吴晓羽, 张姝, 周中华, 李磊, 梁兆光, 李为民 2008 中国心脏起搏与心电生理杂志 22 347]
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