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Spiral dynamics induced by spatiotemporal modulation is investigated in the generic excitable Barkley model. The coexistence of meandering spiral wave and travelling spiral wave in the same medium is discovered under proper spatiotemporal modulation. The underlying mechanism behind this coexistence phenomenon is analyzed. And the two necessary conditions which are needed to observe the coexistence of meandering spiral wave and travelling spiral wave in the excitable Barkley model are discussed.
[1] Walgraef D 1997 Spatio-Temporal Pattern Formation (New York: Springer Verlag)
[2] Winfree A T 1987 When Time Breaks Down (New Jersey: Princeton University Press)
[3] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[4] Winfree A T 1972 Science 175 634
[5] Comacho P, Lechleiter J D 1993 Science 260 226
[6] Huang X Y, Troy W C, Yang Q, Ma H T, Laing C R, Schiff S J, Wu J X 2004 The Journal of Neuroscience 24 9897
[7] Ma J, Tang J, Zhang A H, Jia Y 2010 Sci. China Phys. Mech. Astron. 53 672
[8] Ma J, Zhang A H, Tang J, Jin W Y 2010 J. Bio. Sys. 18 243
[9] Ma J, Wu Y, Ying H P, Jia Y 2011 Chinese Sci. Bull. 56 151
[10] Qian Y 2012 Chin. Phys. B 21 088201
[11] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[12] Qu Z L, Kil J, Xie F G, Garfinkel A, Weiss J N 2000 Bio. Phys. J. 78 2761
[13] Kanakov O I, Osipov G V, Chan C, Kurths J 2007 Chaos 17 015111
[14] Sinha S, Pande A, Pandit R 2001 Phys. Rev. Lett. 86 3678
[15] Alonso S, Sagues F, Mikhailov A S 2003 Science 299 1722
[16] Zhang H, Cao Z J, Wu N J, Ying H P, Hu G 2005 Phys. Rev. Lett. 94 188301
[17] Xiao J H, Hu G, Zhang H, Hu B 2005 Euro Phys. Lett. 69 29
[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 物理学报 55 4420]
[19] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 190501 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 190501]
[20] 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 物理学报 60 080503]
[21] Zhang H, Wu N J, Ying H P, Hu G, Hu B 2004 J. Chem. Phys. 121 7276
[22] Chen J X, Zhang H, Li Y Q 2006 J. Chem. Phys. 124 014505
[23] Deng B W, Zhang G Y, Chen Y 2009 Commun. Theor. Phys. 52 173
[24] Yuan G Y 2011 Commun. Theor. Phys. 56 467
[25] Qian Y 2012 Acta Phys. Sin. 61 158202 (in Chinese) [钱郁 2012 物理学报 61 158202]
[26] Barkley D, Kness M, Tuckerman L 1990 Phys. Rev. A 42 2489
[27] Aliev R R, Panfilov A V 1996 Chaos, Solitions and Fractals 7 293
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[1] Walgraef D 1997 Spatio-Temporal Pattern Formation (New York: Springer Verlag)
[2] Winfree A T 1987 When Time Breaks Down (New Jersey: Princeton University Press)
[3] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[4] Winfree A T 1972 Science 175 634
[5] Comacho P, Lechleiter J D 1993 Science 260 226
[6] Huang X Y, Troy W C, Yang Q, Ma H T, Laing C R, Schiff S J, Wu J X 2004 The Journal of Neuroscience 24 9897
[7] Ma J, Tang J, Zhang A H, Jia Y 2010 Sci. China Phys. Mech. Astron. 53 672
[8] Ma J, Zhang A H, Tang J, Jin W Y 2010 J. Bio. Sys. 18 243
[9] Ma J, Wu Y, Ying H P, Jia Y 2011 Chinese Sci. Bull. 56 151
[10] Qian Y 2012 Chin. Phys. B 21 088201
[11] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[12] Qu Z L, Kil J, Xie F G, Garfinkel A, Weiss J N 2000 Bio. Phys. J. 78 2761
[13] Kanakov O I, Osipov G V, Chan C, Kurths J 2007 Chaos 17 015111
[14] Sinha S, Pande A, Pandit R 2001 Phys. Rev. Lett. 86 3678
[15] Alonso S, Sagues F, Mikhailov A S 2003 Science 299 1722
[16] Zhang H, Cao Z J, Wu N J, Ying H P, Hu G 2005 Phys. Rev. Lett. 94 188301
[17] Xiao J H, Hu G, Zhang H, Hu B 2005 Euro Phys. Lett. 69 29
[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 物理学报 55 4420]
[19] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 190501 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 190501]
[20] 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 物理学报 60 080503]
[21] Zhang H, Wu N J, Ying H P, Hu G, Hu B 2004 J. Chem. Phys. 121 7276
[22] Chen J X, Zhang H, Li Y Q 2006 J. Chem. Phys. 124 014505
[23] Deng B W, Zhang G Y, Chen Y 2009 Commun. Theor. Phys. 52 173
[24] Yuan G Y 2011 Commun. Theor. Phys. 56 467
[25] Qian Y 2012 Acta Phys. Sin. 61 158202 (in Chinese) [钱郁 2012 物理学报 61 158202]
[26] Barkley D, Kness M, Tuckerman L 1990 Phys. Rev. A 42 2489
[27] Aliev R R, Panfilov A V 1996 Chaos, Solitions and Fractals 7 293
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