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| Reconnection Probability of Small World Networks Affects the Ability of Spiral Wave to Go Through Defect |
| WANG Linnaa, TANG Wenzhonga, WANG Yanyangb, ZHANG Mingminga
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| a. School of Computer Science, Beihang University, Beijing 100191, China; b. School of Aeronautical Science and Engineering, Beihang University, Beijing 100191, China |
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Abstract Based on improved Greenberg-Hastings cellular automaton model, this paper built a complex neural network model and studied the effects of reconnection probability p on the ability of penetrating defect of spiral wave under two kinds of classical small world network. It shows that when p is less than or equals a fixed value pc, the ability of penetrating defect of spiral waves will markedly enhance with the increase of reconnection probability p; When p is greater than the pc, the ability of penetrating defect of spiral waves will not enhance with the increase of p.
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Received: 25 April 2014
Published: 25 February 2025
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[1] Biktashev V N, Holden A V. Reentrant waves and their elimination in a model of mammalian ventricular tissue[J].Chaos: an Interdisciplinary Journal of Nonlinear Science, 1998, 8(1): 48-56. [2] Ouyang Q, Flesselles J M. Transition from spirals to defect turbulence driven by a convective instability[J].Nature, 1996, 379(6561):143-146. [3] Ouyang Q, Swinney H L, Li G. Transition from spirals to defect-mediated turbulence driven by a doppler instability.[J].Physical Review Letters, 2000, 84(5):1047-1050. [4] Lu Q Z, Qi O. Experimental studies on long-wavelength instability and spiral breakup in a reaction-diffusion system[J].Physical Review Letters, 2000, 85(8):1650-1653. [5] Stamp A T, Osipov G V, Collins J J. Suppressing arrhythmias in cardiac models using overdrive pacing and calcium channel blockers.[J].Chaos, 2002, 12(3):931-940. [6] Bar M, Brusch L, Or-Guil M. Mechanism for spiral wave breakup in excitable and oscillatory media[J].Phys Rev Lett, 2004;92:119801. [7] Li B W, Gao X, Deng Z G, et al. Circular-interface selected wave patterns in the complex Ginzburg-Landau equation[J].Epl, 2010, 91(3):34001-34006(6). [8] Luo J M, Zhan M. Electric-field-induced wave groupings of spiral waves with oscillatory dispersion relation[J].Physical Review E, 2008, 78(1):1302-1314. [9] Wang X F, Li X C, Dong Lifang. Controlling spiral wave with target wave in oscillatory systems[J].Acta Physica Sinica, 2007, 16(9):2640-2643. [10] 尹小舟, 刘勇. 非连续反馈控制激发介质中的螺旋波[J].物理学报, 2008, 57(11):6844-6851. Yin Xiaozhou, Liu Yong. Suppression of spiral wave in the excitable media by using intermittent feedback scheme[J].Acta Phys Sin, 2008, 57(11):6844-6851. [11] Ma J, Jin W Y, Yi M, et al. Control of spiral wave and turbulence in the time-varied reaction-diffusion system[J].Acta Physica Sinica, 2008, 57(5):2832-2841. [12] Ma J, Ying H P, Liu Y, et al. Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space[J].Acta Phys Sin, 2009, 18(1):98-105. [13] Zhang Lisheng, Deng Minyi, Kong Lingjiang, et al. Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics: cellular automaton simulations for target waves in excitable media[J].Communications in Theoretical Physics, 2010, 53(1):171-174. [14] Wasserman S. Social Network Analysis: Methods and Applications[M].Cambridge: Cambridge University Press, 1994. [15] Wu J, Watts D J. Small worlds: the dynamics of networks between order and randomness.[J].Sigmod Record, 1999, 31(2):74-75. [16] Daihai H, Gang H, Meng Z, et al. Pattern formation of spiral waves in an inhomogeneous medium with small-world connections.[J].Physical Review E Statistical Nonlinear & Soft Matter Physics, 2002, 65(5Pt2):126-126. [17] Orit S, Ido G, Ronen S, et al. Morphological characterization of in vitro neuronal networks[J].Physical Review E Statistical Nonlinear & Soft Matter Physics, 2002, 66(2):1039-1044. [18] 甘正宁, 马军, 张国勇, 等. 小世界网络上螺旋波失稳的研究[J].物理学报, 2008, 57(9), 5400-5406. Gan Zhengning, Ma Jun, Zhang Guoyong, et al. Instability of spiral wave in small-world networks[J].Acta Phys Sin, 2008, 57(9), 5400-5406. [19] 马军, 唐军, 张爱华, 等. 二维格子神经元网络中螺旋波的鲁棒性和破裂[J].中国科学, 2009, (12):1754-1761. Ma Jun, Tang Jun, Zhang Aihua, et al. Robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons[J].Sci China Phys Mech Astron, 2009, (12):1754-1761. [20] 宋宣玉, 钱郁, 陈光旨,等. 不同缺陷对周期螺旋波的影响[J].广西物理, 2007,(1):7. Song Xunayu, Qian Yu, Chen Guangzhi, et al. The effect of different defects on the periodic spiral wave[J].Guangxi Physics, 2007,(1):7. [21] Hendrey M, Ott E, Antonsen T M. Effect of inhomogeneity on spiral wave dynamics[J].Physical Review Letters, 1999, 82(4): 859-862. [22] Hendrey M, Ott E, Antonsen T M. Spiral wave dynamics in oscillatory inhomogeneous media[J].Physical Review E, 2000, 61(5): 4943. [23] Xie F, Qu Z, Weiss J N, et al. Coexistence of multiple spiral waves with independent frequencies in a heterogeneous excitable medium[J].Physical Review E, 2001, 63(3): 031905. [24] 田昌海, 邓敏艺, 孔令江, 等. 螺旋波动力学性质的元胞自动机有向小世界网络研究[J].物理学报, 2011, 60(8): 80505-080505. Tian Changhai, Deng Minzhi, Kong Lingjiang, et al. Cellular automaton simulation with directed small-world networks for the dynamical behaviors of spiral waves[J].Acta Phys Sin, 2011, 60(8):80505-080505. [25] 戴瑜, 唐国宁. 离散可激发介质激发性降低的几种起因[J].物理学报, 2009, 58(3): 1491-1496. Dai Yu, Tang Guoning. Some origins of the low excitability of a discrete excitable medium[J].Acta Phys Sin, 2009, 58(3):1491-1496. |
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