时空调制对可激发介质螺旋波波头动力学行为影响及控制研究

The influence of spatiotemporal modulation on spiral tip dynamics in excitable medium and its application for spiral control

本文首先研究了时空调制对可激发介质中周期螺旋波波头动力学行为的影响.随着时空调制的增大,螺旋波经历了周期螺旋波、外滚螺旋波、旅行螺旋波和内滚螺旋波的显著变化.通过定义序参量来定量的描述由时空调制引起的螺旋波在不同态之间非平衡跃迁的临界条件,及漫游螺旋波波头圆滚圆半径随调制参数的变化情况.当时空调制增大到某个临界值时,螺旋波发生了破碎;再增加时空调制,螺旋波则发生了衰减,系统最终演化为空间均匀静息态.在文中给出了螺旋波发生破碎和衰减的机理和原因.最后将时空调制方法运用于漫游螺旋波,实现了将漫游螺旋波控制成周期螺旋波,或将其控制为空间均匀静息态.

In this paper,the influence of spatiotemporal modulation on tip dynamics of periodic spiral wave in excitable medium is studied first.By varying spatiotemporal modulation item,the dynamics of spiral wave changes dramatically and the system undergoes periodic spiral wave,epicycloid meandering spiral wave,traveling spiral wave and hypocycloid meandering spiral wave.An order parameter is introduced to detect the critical conditions of non-equilibrium transition between different patterns.And the variation of spiral tip radius induced by spatiotemporal modulation can also be reflected by this order parameter.When spatiotemporal modulation increases to a critical value,spiral waves break up.And spiral waves will damp to homogeneous rest state if spatiotemporal modulation increases further.The mechanisms of spiral breakup and damping are explained in the paper.Finally we apply the spatiotemporal modulation method to the meandering spiral waves and can successfully control meandering spiral waves into periodic spiral waves or homogeneous rest state.