Spiral Wave Dynamics of Excited Medium: Effect of Relative Refractory

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

Abstract

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

CLC Number:

O415.6

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.

Figures/Tables 5

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)

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

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

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.)

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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