激发介质相对不应态对螺旋波动力学行为的影响

doi:10.19596/j.cnki.1001-246x.8321

摘要/Abstract

摘要：

采用元胞自动机模型研究激发介质相对不应态对螺旋波动力学行为的影响。数值模拟表明：元胞激发阈值存在一临界区间，该区间的螺旋波周期会突然增加，并存在一最大周期，在合适的系统尺寸和状态数下，螺旋波周期不再受相对不应态的影响而只取决于系统的激发阈值；相对不应态导致螺旋波“Z”型漫游、小范围无规律漫游、花瓣状漫游、锯齿状漫游、风车状漫游等复杂的波头运动。观察到稳定螺旋波、漫游螺旋波和螺旋波消失，并对产生这些现象的机制作简要的解释。

关键词: 激发介质, 相对不应态, 螺旋波, 元胞自动机, 数值模拟

Abstract:

Effect of relative refractory of excited medium on dynamical behavior of spiral waves is investigated in a cellular automata model. It is found that there is a critical interval in the excitation threshold. Spiral wave period in the critical interval increases suddenly and there is a maximum period. Under appropriate system size and number of states, the spiral wave period is not affected by refractoriness. It depends on the excitation threshold of the system only. Relative refractory state leads to Z-type meandering, small-scale irregular meandering, petal meandering, jagged meandering, windmill meandering and other complex spiral wave tip motions. Stable spiral wave, meandering spiral wave, and disappearing spiral wave are observed. Mechanisms of these phenomena are briefly analyzed.

Key words: excitable medium, relative refractory state, spiral wave, cellular automata, numerical simulation

中图分类号:

O415.6

关富荣, 李成乾, 邓敏艺. 激发介质相对不应态对螺旋波动力学行为的影响[J]. 计算物理, 2021, 38(6): 749-756.

Furong GUAN, Chengqian LI, Minyi DENG. Spiral Wave Dynamics of Excited Medium: Effect of Relative Refractory[J]. Chinese Journal of Computational Physics, 2021, 38(6): 749-756.

图/表 5

图1 相对不应态对螺旋波周期的影响(a)~(c)分别是截断行波后1000时步、2000时步、3000时步的螺旋波斑图(Ra=12, Rr=3, Thq=30); (d)T随Thq的变化(Tha=76)

Fig.1 Effect of relative refractory states on the period of spiral wave (a)-(c) are the spiral wave patterns at 1000, 2000, and 3000 time steps after truncating the traveling wave (Ra=12, Rr=3, Thq=30); (d) Change of period T with time(Tha=76)

图2 不同m, n下T随Thq的变化(Tha=76) (a)m=100, n=10; (b)m=300, n=15; (c)m=300, n=25; (d)m=400, n=25

Fig.2 Spiral wave period T varies with Thq under different m and n (Tha=76) (a)m=100, n=10; (b)m=300, n=15; (c)m=300, n=25; (d)m=400, n=25

图3 相对不应态对螺旋波波头轨迹的影响(Ra=25 - Rr, Thq=30, Tha=76) (a)Rr=0; (b)Rr=4; (c)Rr=9; (d)Rr=13; (e)Rr=14; (f)Rr=16; (g)Rr=20; (h)Rr=21

Fig.3 Effect of the relative refractory state on the trajectory of the spiral wave tip (Ra=25 - Rr, Thq=30, Tha=76) (a) Rr=0; (b)Rr=4; (c)Rr=9; (d)Rr=13; (e)Rr=14; (f)Rr=16; (g)Rr=20; (h)Rr=21

图4 不同(Rr, Ra)下的螺旋波演化结果(Thq=30，Tha=76) (□代表稳定螺旋波; ○代表螺旋波作周期漫游; ▲代表螺旋波作准周期漫游螺旋波; ▼代表螺旋波作非周期漫游; ☆代表螺旋波消失; ◇代表螺旋波破碎。)

Fig.4 Evolution behavior of spiral waves under different (Rr, Ra) (Thq=30, Tha=76) (□, ○, ▲, ▼, ☆, ◇ represent stable spirals, periodic meandering spirals, quasiperiodic meandering spirals, aperiodic meandering spirals, disappearance and breakup of spiral waves, respectively.)

图5 相对不应态导致的螺旋波消失(Ra=10，Rr=15，Thq=30，Tha=76)，(a)~(d)分别为t=10 000、11 909、11 912、11 970时的元胞状态灰度图，元胞状态值越大，对应的点就越明亮；(e)为(20, 20)处元胞的状态随时间的变化

Fig.5 Disappearance of spiral wave caused by relative refractory state (Ra=10, Rr=15, Thq=30, Tha=76) (a)-(d) are grayscale images of cell state at t=10 000, 11 909, 11 912, and 11 970. The larger the cellular state value is, the brighter the corresponding point will be; (e)Change of cellular state with time at (20, 20)

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