Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

doi:10.1088/1674-1056/20/4/040503

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40503-040503.doi: 10.1088/1674-1056/20/4/040503

Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

袁国勇

Department of Physics, Hebei Normal University, Shijiazhuang 050016, China;Hebei Advanced Thin Films Laboratory, Shijiazhuang 050016, China

收稿日期:2010-11-02 修回日期:2010-12-30 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11005030), the Science Foundation of Hebei Education Department, China (Grant No. 2009135), the Science Foundation of Inner Mongolia Education Department, China (Grant No. NJ09178) and the Science Foundation of Hebei Normal University, China.

Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

Yuan Guo-Yong(袁国勇)^a)b)^†

^aDepartment of Physics, Hebei Normal University, Shijiazhuang 050016, China; ^bHebei Advanced Thin Films Laboratory, Shijiazhuang 050016, China

Received:2010-11-02 Revised:2010-12-30 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11005030), the Science Foundation of Hebei Education Department, China (Grant No. 2009135), the Science Foundation of Inner Mongolia Education Department, China (Grant No. NJ09178) and the Science Foundation of Hebei Normal University, China.

摘要/Abstract

摘要： We numerically study the dynamics of spiral waves in the excitable system with the excitability modulated by a rectangle wave. The tip trajectories and their variations with the modulation period T are explained by the corresponding spectrum analysis. For a large T, the external modulation leads to the occurrence of more frequency peaks and these frequencies change with the modulation period according to their specific rules, respectively. Some of the frequencies and a primary frequency f₁ determine the corresponding curvature periods, which are locked into rational multiplies of the modulation period. These frequency-locking behaviours and the limited life-span of the frequencies in their variations with the modulation period constitute many resonant entrainment bands in the T axis. In the main bands, which follow the relation T/T₁₂=m/n, the size variable R_x of the tip trajectory is a monotonic increasing function of T. The rest of the frequencies are linear combinations of the two ones. Due to the complex dynamics, many unique tip trajectories appear at some certain T. We find also that spiral waves are eliminated when T is chosen from the end of the main resonant bands. This offers a useful method of controling the spiral wave.

关键词: spiral wave, FitzHugh--Nagumo model, frequency-locking

Abstract: We numerically study the dynamics of spiral waves in the excitable system with the excitability modulated by a rectangle wave. The tip trajectories and their variations with the modulation period T are explained by the corresponding spectrum analysis. For a large T, the external modulation leads to the occurrence of more frequency peaks and these frequencies change with the modulation period according to their specific rules, respectively. Some of the frequencies and a primary frequency f₁ determine the corresponding curvature periods, which are locked into rational multiplies of the modulation period. These frequency-locking behaviours and the limited life-span of the frequencies in their variations with the modulation period constitute many resonant entrainment bands in the T axis. In the main bands, which follow the relation T/T₁₂=m/n, the size variable R_x of the tip trajectory is a monotonic increasing function of T. The rest of the frequencies are linear combinations of the two ones. Due to the complex dynamics, many unique tip trajectories appear at some certain T. We find also that spiral waves are eliminated when T is chosen from the end of the main resonant bands. This offers a useful method of controling the spiral wave.

Key words: spiral wave, FitzHugh--Nagumo model, frequency-locking

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.65.+b (Self-organized systems) 47.54.-r (Pattern selection; pattern formation)

袁国勇. Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave[J]. 中国物理B, 2011, 20(4): 40503-040503.

Yuan Guo-Yong(袁国勇) . Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave[J]. Chin. Phys. B, 2011, 20(4): 40503-040503.

参考文献 49

[1]	Courtemanche M 1996 Chaos 6 579
[2]	Nettesheim S, Oertzen A V, Rotermund H H and Ertl G 1993 J. Chem. Phys. 98 9977
[3]	Frisch T, Rica S, Coullet P and Gilli J M 1994 Phys. Rev. Lett. 72 1471
[4]	Van Oss C, Panfilov A V, Hogeweg P, Siegert F and Weijer C J 1996 J. Theor. Biol. 181 203
[5]	Winfree A T and Strogatz S H 1983 Physica D 8 35
[6]	Ouyang Q, Swinney H L and Li G 2000 Phys. Rev. Lett. 84 1047
[7]	Zhou L Q and Ouyang Q 2000 Phys. Rev. Lett. 85 1650
[8]	Zhang H, Ruan X S, Hu B and Ouyang Q 2004 Phys. Rev. E 70 016212
[9]	Tang G N, Deng M Y, Hu B and Hu G 2008 Phys. Rev. E 77 046217
[10]	Wu N J, Zhang H, Ying H P, Cao Z J and Hu G 2006 Phys. Rev. E 73 060901R
[11]	Kim M, Bertram M, Pollmann M, Oertzen A, Mikhailov A S, Rotermund H H and Ertl G 2001 Science 292 1357
[12]	Sakaguchi H and Fujimoto T 2003 Phys. Rev. E 67 067202
[13]	Wang P Y and Xie P 2000 Phys. Rev. E 61 5120
[14]	Zhang H, Cao Z, Wu N J, Ying H P and Hu G 2005 Phys. Rev. Lett. 94 188301
[15]	Yuan G Y, Wang G R and Chen S G 2005 Europhys. Lett. 72 908
[16]	Yuan G Y, Chen S G and Yang S P 2007 Euro. Phys. J. B 58 331
[17]	Ma J, Wang C N, Jin W Y, Li Y L and Pu Z S 2008 Chin. Phys. B 17 2844
[18]	Wang J, Kádár S, Jung P and Showalter K 1999 Phys. Rev. Lett. 82 855
[19]	Garc'hia-Ojalvo J and Schimansky-Geier L 1999 Europhys. Lett. 47 298
[20]	Maselko J and Showalter K 1991 Physica D 49 21
[21]	Lindner B, Garc'hia-Ojalvo J, Neiman A and Schimansky-Geier L 2004 Phys. Rep. 392 321
[22]	Sagués F, Sancho J M and Garc'hia-Ojalvo J 2007 Rev. Mod. Phys. 79 829
[23]	Jung P and Mayer-Kress G 1995 Chaos 5 458
[24]	Jung P and Mayer-Kress G 1995 Phys. Rev. Lett. 74 2130
[25]	Jung P 1997 Phys. Rev. Lett. 78 1723
[26]	Jung P, Cornell-Bell A, Madden K and Moss F 1998 J. Neurophysiol. 79 1098
[27]	Kádár S, Wang J and Showalter K 1998 Nature 391 770
[28]	Hempel H, Schimansky-Geier L and Garc'hia-Ojalvo J 1999 Phys. Rev. Lett. 82 3713
[29]	Winfree A T 1991 Chaos 1 303
[30]	Sendi na-Nadal I, Alonso S, Pérez-Mu nuzuri V, Gómez-Gesteira M, Pérez-Villar V, Ram'hirez-Piscina L, Casademunt J, Sancho J M and Sagués F 2000 Phys. Rev. Lett. 84 2734
[31]	Steinbock O, Zykov V S and Müller S C 1993 Nature 366 322
[32]	Braune M and Engel H 2000 Phys. Rev. E 62 5986
[33]	Zykov V S, Kheowan O U, Rangsiman O and Müller S C 2002 Phys. Rev. E 65 026206
[34]	Kheowan O U, Zykov V S, Rangsiman O and Müller S C 2001 Phys. Rev. Lett. 86 2170
[35]	Zykov V S, Brandtstädter H, Bordiougov G and Engel H 2005 Phys. Rev. E 72 065201R
[36]	Zykov V S, Bordiougov G, Brandtstädter H, Gerdes I and Engel H 2004 Phys. Rev. Lett. 92 018304
[37]	Zykov V S and Engel H 2004 Phys. Rev. E 70 016201
[38]	Kheowan O U, Kantrasiri S, Wilairat P, Storb U and Müller S C 2004 Phys. Rev. E 70 046221
[39]	Kheowan O U, Kantrasiri S, Uthaisar C, Gáspár V and Müller S C 2004 Chem. Phys. Lett. 389 140
[40]	Naknaimueang S, Allen M A and Müller S C 2006 Phys. Rev. E 74 066209
[41]	Zykov V S and Engel H 2004 Physica D 199 243
[42]	Yuan G Y, Xu A G, Wang G R and Chen S G 2010 Europhys. Lett. 90 10013
[43]	Braune M and Engel H 1993 Chem. Phys. Lett. 211 534
[44]	Markus M, Nagy-Ungvarai Z and Hess B 1992 Science 257 225
[45]	Steinbock O, Schütze J and Müller S C 1992 Phys. Rev. Lett. 68 248
[46]	Agladze K I and De Kepper P 1992 J. Phys. Chem. 96 5239
[47]	Mu nuzuri A P, Gómez-Gesteira M, Pérez-Mu nuzuri V, Krinsky V I and Pérez-Villar V 1993 Phys. Rev. E 48 R3232
[48]	Mu nuzuri A P, Innocenti C, Flesselles J M, Gilli J M, Agladze K I and Krinsky V I 1994 Phys. Rev. E 50 R667
[49]	FitzHugh R 1961 Biophys. J. 1 445

Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

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