螺旋波动力学性质的元胞自动机有向小世界网络研究

Cellular automaton simulation with directed small-world networks for the dynamical behaviors of spiral waves

以Greenberg-Hastings激发介质元胞自动机模型为基础,研究了有向小世界网络中重新连接概率p对螺旋波动力学行为的影响.对于在规则网络下的稳定螺旋波,施加有向小世界网络后发现:当p值较小时,原本稳定的螺旋波仍保持其稳定性.随着p的增大,先后观察到螺旋波持续漫游、螺旋波断裂以及螺旋波消失等现象.通过监测系统的激发比率,发现以上现象的产生源于介质激发性随p的增大而降低.同时还发现元胞周期的变化也与p有关.

In this paper,we study the influence of the rewiring probability p of the directed small-world network on dynamical behavior of spiral wave using the Greenberg-Hastings cellular automaton model.The computer simulation results show that when p is small enough,the stable spiral wave under the regular networks keeps its stability unchanged,and when p is increased,the phenomenon such as meandering,breakup and disappearance of the spiral waves appears.The relation between the excitability and p leads to the conclusion that the occurrence of the above phenomenon originates from the reducing of the excitability.On the other hand,the period of cell is also related to p.