多可激性障碍下的螺旋波动力学

Spiral-wave dynamics in an excitable medium with many excitability obstacles

在许多实际可激系统中局部不均匀是广泛存在的,它们是螺旋波形成以及动力学行为改变的重要因素.本文研究了可激性障碍对螺旋波动力学行为的影响.研究表明,在障碍区域内可激性参数大于区域外情况下障碍会对其附近的螺旋波波头有吸引作用,多局部障碍共存时吸引行为不仅依赖障碍分布,而且依赖障碍的大小以及区域内可激性参数的具体取值.通过抑制变量小值区域的变化分析了这些行为发生的原因.在障碍区域内可激性参数小于区域外情况下障碍对其近邻的螺旋波波头有排斥作用,排斥后波头的运动依赖初始螺旋波是刚性旋转的还是漫游的.多局部障碍共存时排斥作用对螺旋波动力学行为的改变依赖障碍的分布、大小与区域内可激性参数的具体取值以及初始螺旋波的类型.

Many real excitable systems can be descibed as inhomogeneous media, where the inhomogeneity is an important factor for the formation of spiral waves and the changing of their dynamics. In this paper, we investigate the effect of excitability obstacles on spiral-wave dynamics. For an excitability-reduced obstacle, the neighbor spiral tip is attracted into the obstacle. When more localized obstacles are placed, the attactive case depends on the distribution, size and excitability of the obstcales. On the basis of analyzing the small-value area of the inhibitor variable, we illustrate the mechanism of these behaviors occuring. For an excitability-enhanced obstacle, the nearby spiral tip is repelled. The tip motion after the repelsive effect depends on the type of the initial spiral wave, i.e. rigidily rotating spiral wave or meandering spiral wave. In the present of more localized obstacles, there exist different behaviors for different distributions, sizes and exeitabilities of the obsteales, and different types of initial waves.