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本文首先研究了时空调制对可激发介质中周期螺旋波波头动力学行为的影响. 随着时空调制的增大, 螺旋波经历了周期螺旋波、外滚螺旋波、旅行螺旋波和内滚螺旋波的显著变化. 通过定义序参量来定量的描述由时空调制引起的螺旋波在不同态之间非平衡跃迁的临界条件, 及漫游螺旋波波头圆滚圆半径随调制参数的变化情况. 当时空调制增大到某个临界值时, 螺旋波发生了破碎; 再增加时空调制, 螺旋波则发生了衰减, 系统最终演化为空间均匀静息态. 在文中给出了螺旋波发生破碎和衰减的机理和原因. 最后将时空调制方法运用于漫游螺旋波, 实现了将漫游螺旋波控制成周期螺旋波, 或将其控制为空间均匀静息态.In this paper, the influence of spatiotemporal modulation on tip dynamics of periodic spiral wave in excitable medium is studied first. By varying spatiotemporal modulation item, the dynamics of spiral wave changes dramatically and the system undergoes periodic spiral wave, epicycloid meandering spiral wave, traveling spiral wave and hypocycloid meandering spiral wave. An order parameter is introduced to detect the critical conditions of non-equilibrium transition between different patterns. And the variation of spiral tip radius induced by spatiotemporal modulation can also be reflected by this order parameter. When spatiotemporal modulation increases to a critical value, spiral waves break up. And spiral waves will damp to homogeneous rest state if spatiotemporal modulation increases further. The mechanisms of spiral breakup and damping are explained in the paper. Finally we apply the spatiotemporal modulation method to the meandering spiral waves and can successfully control meandering spiral waves into periodic spiral waves or homogeneous rest state.
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Keywords:
- spiral wave /
- tip trajectory /
- spatiotemporal modulation
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[31] Chen J X, Xu J R, Yuan X P, Ying H P 2009 J. Phys. Chem. B 113 849
[32] Chen J X, Mao J W, Hu B, Xu J R, He Y F, Li Y, Yuan X P 2009 Phys. Rev. E 79 066209
[33] Winfree A T 1973 Science 181 937
[34] Ouyang Q, Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047
[35] Barkley D, Kness M, Tuckerman L 1990 Phys. Rev. A 42 2489
[36] 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] He D H, Shi P L, Stone L W 2003 Phys. Rev. E 67 27201
[4] Perc M 2007 Chaos, Solitons and Fractals 31 280
[5] Wang C N, Ma J, Tang J, Li Y L 2010 Commun Theor Phys. 53 382
[6] Ma J, Wu Y, Ying H P, Jia Y 2011 Chinese Science Bulletin 56 151
[7] Ma J, Wang C N, Jin W Y, Wu Y 2010 Appl. Math. Comput 217 3844
[8] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[9] Winfree A T 1972 Science 175 634
[10] Ouyang Q, Flesselles J M 1996 Nature 379 143
[11] Comacho P, Lechleiter J D 1993 Science 260 226
[12] Oss C V, Panfilov A V, Hogeweg P, Siegert F, Weiger C J 1996 J. Theor. Biol. 181 201
[13] Dahlem M A, Müller S C 1997 Exp. Brain Res. 115 319
[14] Callamaras N, Marchant J S, Sun X P 1998 J. Physiol. 509 81
[15] Falcke M 2003 New J. Phys. 5 96
[16] Wolff J, Rotermund H H 2003 New J. Phys. 5 60
[17] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[18] Qu Z L, Kil J, Xie F G, Garfinkel A, Weiss J N 2000 Biophys. J. 78 2761
[19] Kanakov O I, Osipov G V, Chan C, Kurths J 2007 Chaos 17 015111
[20] Huang X D, Qian Y, Zhang X M, Hu G 2010 Phys. Rev. E 81 051903
[21] Aranson I, Levine H, Tsimring L 1994 Phys. Rev. Lett. 72 2561
[22] Rappel W J, Fenton F, Karma A 1999 Phys. Rev. Lett. 83 456
[23] Sinha S, Pande A, Pandit R 2001 Phys. Rev. Lett. 86 3678
[24] Alonso S, Sagues F, Mikhailov A S 2003 Science 299 1722
[25] Zhang H, Hu B, Hu G 2003 Phys. Rev. E 68 026134
[26] Zhang H, Cao Z J, Wu N J, Ying H P, Hu G 2005 Phys. Rev. Lett. 94 188301
[27] Xiao J H, Hu G, Zhang H, Hu B 2005 Europhys. Lett. 69 29
[28] 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]
[29] Ma J, Jin W Y, Li Y L, Zheng Y 2007 Acta Phys. Sin. 56 2456 (in Chinese) [马军, 靳伍银, 李延龙, 陈勇 2007 物理学报 56 2456]
[30] Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[31] Chen J X, Xu J R, Yuan X P, Ying H P 2009 J. Phys. Chem. B 113 849
[32] Chen J X, Mao J W, Hu B, Xu J R, He Y F, Li Y, Yuan X P 2009 Phys. Rev. E 79 066209
[33] Winfree A T 1973 Science 181 937
[34] Ouyang Q, Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047
[35] Barkley D, Kness M, Tuckerman L 1990 Phys. Rev. A 42 2489
[36] Aliev R R, Panfilov A V 1996 Chaos, Solitions and Fractals 7 293
[37] Barkley D 1992 Phys. Rev. Lett. 68 2090
[38] Barkley D 1994 Phys. Rev. Lett. 72 164
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