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采用FitzHugh-Nagumo方程,研究了二维时空系统中螺旋波的控制问题,利用相空间压缩方法对部分系统变量的振幅进行限制从而影响螺旋波的稳定性.研究表明,控制过程可分为三个不同的阶段:在较小压缩限条件下螺旋波可以被完全消除,系统进入均匀定态;在较大的压缩限条件下螺旋波能够稳定存在,而且其振荡频率不随控制参数的改变而发生变化;当压缩限介于上述两者之间时,系统表现为时空混沌态.对上述控制过程进行了进一步的讨论,研究了不同控制参数条件下的系统斑图、变量的演化、相空间轨道等性质,并且对振幅函数和振荡频率特征进
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关键词:
- 螺旋波 /
- 相空间压缩 /
- FitzHugh-Nagumo方程
Control of spiral wave in two-dimensional FitzHugh-Nagumo equation is studied. The phase space compression approach is used to confine the system trajectory into a finite area and to annihilate spiral wave in the numerical simulation. Three stages are found in the control process. The spiral is driven to a homogenous stationary state when the compress limit is small; the spiral is stable with a fixed frequency when the compression limit is large; in the intermediate controlling parameter regime, the spatiotemporal turbulent state is observed. The controlling process is investigated by considering system pattern, variable evolution, phase space trajectory, etc, and the characteristics of amplitude function and oscillatory frequency are summarized as well.-
Keywords:
- spiral wave /
- phase space compression /
- FitzHugh-Nagumo equation
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[1] Kuramoto Y 1984 Chemical Oscillations, Waves and Turbulence (New York: Springer)
[2] Cross M, Hohenberg P 1993 Rev. Mod. Phys. 65 851
[3] [4] Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [欧阳颀 2000 反应扩散系统中的斑图动力学(上海:上海科技教育出版社)]
[5] [6] [7] Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Acta Phys. Sin. 57 5400 (in Chinese) [甘正宁、 马 军、 张国勇、 陈 勇 2008物理学报 57 5400]
[8] Xie L L, Gao J H 2010 Chin. Phys. B 19 060515
[9] [10] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟 敏、 唐国宁 2010 物理学报 59 1593]
[11] [12] Ecke R E, Hu Y C, Mainieri R, Ahlers G 1995 Science 269 1704
[13] [14] [15] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[16] [17] Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174
[18] [19] Winfree A T 1987 When Time Breaks Down (Princeton: Princeton University Press)
[20] [21] Vanag V K, Epstein I R 2001 Science 294 835
[22] [23] Gong Y F, Christini D J 2003 Phys. Rev. Lett. 90 088302
[24] Zaritski R M, Pertsov A M 2002 Phys. Rev. E 66 066120
[25] [26] Goryachev A, Chate H, Kapral R 1998 Phys. Rev. Lett. 80 873
[27] [28] Yuan G Y, Zhang G C, Wang G R, Chen S G 2005 Commun. Theor. Phys. 43 459
[29] [30] Bar M, Eiswirth M 1993 Phys. Rev. E 48 R1635
[31] [32] [33] Brusch L, Torcini A, Bar M 2003 Phys. Rev. Lett. 91 108302
[34] Qian Y, Huang X D, Liao X H, Hu G 2010 Chin. Phys. B 19 050513
[35] [36] Ouyang Q, Flesselles J M 1997 Nature 379 143
[37] [38] [39] Bar M, Or-Guil M 1999 Phys. Rev. Lett. 82 1160
[40] Steinbock O, Schutze J, Muller S C 1992 Phys. Rev. Lett. 68 248
[41] [42] [43] Wang P Y, Xie P 2000 Phys . Rev. E 61 5120
[44] Liu F C, Wang X F, Li X C, Dong L F 2007 Chin. Phys. B 16 2640
[45] [46] Yuan G Y, Yang S P, Wang G R, Chen S G 2008 Chin. Phys. B 17 1925
[47] [48] Zhang H, Hu B, Hu G 2003 Phys. Rev. E 68 026134
[49] [50] [51] 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]
[52] Luo X S 1999 Acta Phys. Sin. 48 402 (in Chinese) [罗晓曙 1999物理学报 48 402]
[53] [54] [55] Zhang X, Shen K 2001 Phys. Rev. E 63 046212
[56] Ma J, Wu N J, Ying H P, Pu Z S 2006 Chin. J. Comput. Phys. 23 243 (in Chinese) [马 军、 吴宁杰、 应和平、 蒲忠胜 2006 计算物理 23 243]
[57] [58] [59] Gao J H, Peng J H 2007 Chin. Phys. Lett. 24 1614
[60] [61] Gao J H, Zheng Z G, Ma J 2008 Int. J. Mod. Phys. B 22 3855
[62] Ma J, Jia Y, Yi M, Tang J, Xia Y F 2009 Chaos Solitons Fract. 41 1331
[63] [64] [65] Yin X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟、 刘 勇 2008 物理学报 57 6844]
[66] [67] Li B W, Zhang H, Ying H P, Hu G 2009 Phys. Rev. E 79 026220
[68] Wang B Y, Xu W, Xing Z C 2009 Acta Phys. Sin. 58 6590 (in Chinese) [王宝燕、 徐 伟、 邢真慈 2009 物理学报 58 6590]
[69] [70] Gao J H, Zhan M 2008 Commun. Theor. Phys. 49 669
[71] [72] [73] Gao J H, Xie L L, Zou W, Zhan M 2009 Phys. Rev. E 79 056214
[74] [75] Gao J H, Xie L L, Peng J H 2009 Acta Phys. Sin. 58 5218 (in Chinese) [高继华、谢玲玲、彭建华 2009 物理学报 58 5218]
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