Journal of Guangxi Normal University(Natural Science Edition) ›› 2016, Vol. 34 ›› Issue (2): 8-14.doi: 10.16088/j.issn.1001-6600.2016.02.002

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Effect of Position Perturbation for Spiral Waves in Excitable Media

DAI Jingyu, ZHANG Xueliang, DENG Minyi, TAN Huili   

  1. College of Physical Science and Technology, Guangxi Normal University, Guilin Guangxi 541004, China
  • Received:2015-12-15 Published:2018-09-14

Abstract: Based on the Greenberg-Hastings cellular automata model, the effect of the position perturbation for the spiral waves in excitable media is studied. The amplitude of the position perturbation represents the interaction distance between cells. The computer simulation results show that the position perturbations with different amplitudes are added into the system after the stable spiral wave is formed, and the stability of spiral wave meanders is related to the range of the position perturbation of the cells. Different ranges of the position perturbation will result in two different changes of the stable waves. New stable waves are formed or disappeared after meanders. The two types meandering behavior are observed, and the mechanism underlying these phenomena are analyzed.

Key words: excitable media, spiral wave, position perturbation, cellular automata model

CLC Number: 

  • O411.3
[1] GERHARDT M, SCHUSTER H, TYSON J J. A cellular automaton model of excitable media including curvature and dispersion[J]. Science, 1990, 247(4950): 1563-1566.
[2] DAVIDENKO J M, KENT P F, CHIALVO D R, et al. Sustained vortex-like waves in normal isolated ventricular muscle[J]. Proceedings of the National Academy of Sciences, 1990, 87: 8785-8789.
[3] DAVIDENKO J M, PERTSOV A V, SALOMONSZ R, et al. Stationary and driftingspiral waves of excitation in isolated cardiac muscle[J]. Nature, 1992, 355: 349-351.
[4] NASH M P, PANFILOV A V. Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias[J]. Progress in Biophysics and Molecular Biology, 2004, 85(2): 501-522.
[5] 欧阳颀. 反应扩散系统中螺旋波的失稳[J]. 物理, 2001, 30(1): 30-35.
[6] CHEN J X, HU B. Spiral breakup and consequent patterns induced by strong polarized advective field[J]. Europhysics Letters, 2008, 84(3): 34002.
[7] LIU G Q, WU N J, YING H P. The drift of spirals under competitive illumination in an excitable medium[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(9): 2398-2401.
[8] 钟敏,唐国宁.限制钾离子电流抑制心脏中螺旋波和时空混沌[J].广西师范大学学报(自然科学版),2010, 28(2): 6-8.
[9] 马军,应和平,李延龙,等.混沌信号驱动实现螺旋波和时空混沌抑制[J].郑州大学学报(理学版),2006,38(1): 45-49.
[10] JIMÈNEZ Z A, MARTS B, STEINBOCK O. Pinned scroll rings in an excitable system[J]. Physcial Review Letters, 2009, 102(24): 244101.
[11] 戴瑜, 韦海明, 唐国宁. 非均匀激发介质中螺旋波的演化[J]. 物理学报, 2010,59(9): 5979-5983.
[12] HE D H, HU G, ZHAN M, et al. Pattern formation of spiral waves in an inhomogeneous medium with small-world connections[J]. Physcial Review E, 2002, 65(5): 055204.
[13] FELDMAN A, YIN J Z, SAXBERG B E H, et al. Vortex wave stability in homogeneous excitable media: Simulations on a randomized discrete iscrete lattice[J]. Engineering in Medicine and Biology Society, 1995, 1: 25-26.
[14] DILLON S M, ALLESSIE M A, URSELL P C, et al. Influences of anisotropic tissue structure on reentrant circuits in the epicardial border zone of subacute canine infarcts[J]. Circulation Research, 1988, 63(1): 182-206.
[15] HOYT R H, COHEN M L, SAFFITZ J E. Distribution and three-dimensional structure of intercellular junctions in canine myocardium[J]. Circulation Research, 1989, 64(3): 563-574.
[16] LUKE R A, SAFFITZ J E. Remodeling of ventricular conduction pathways in healed canine infarct border zones[J]. Journal of Clinical Investigation, 1991, 87(5): 1594-1602.
[17] 田兴玲,刘慕仁,郭俊华.小世界网络上的差额选举模型[J].郑州大学学报(理学版),2008,40(2):60-65.
[18] 梁玉娟.从动能损失看弯道路段的通行能力[J].四川师范大学学报(自然科学版),2011,34(3):355-359.
[19] DENG M Y, CHEN X Q, TANG G N. The effect of cellular aging on the dynamics of spiral waves[J]. Chin Phys B, 2014, 23(12): 120503.
[20] GREENBERG J M, HASTINGS S P. Spatial patterns for discrete models of diffusion in excitable media[J]. SIAM J Appl Math, 1978, 34(3): 515-523.
[21] ZHAO Y, BILLINGS S A, ROUTH A F. Identification of the Belousov-Zhabotingskii reaction using cellular automata[J]. International Journal of Bifurcation and Chaos, 2007, 17(5): 1687-1701.
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