非连续反馈控制激发介质中的螺旋波

Suppression of spiral wave in the excitable media by using intermittent feedback scheme

采用非连续反馈方法来控制Fitz-Hugh-Nagumo方程描述的激发介质中的螺旋波.在控制过程中,对于系统各个格点快变量的幅值进行观测并和设定的阈值进行比较,当采样格点的快变量的值大于这个阈值时,则对系统进行直接小幅度的负反馈.研究发现:在对系统所有格点快变量幅值观测时选择比较小的阈值则更容易将系统的螺旋波消除掉并使系统达到稳定均匀态.在比较大的阈值下,系统的螺旋波则变得稀疏,也可以导致螺旋波的破裂.在任意选择单个格点的快变量观测下,比较小的反馈强度仍然可以消除螺旋波,系统也达到稳定均匀态.当整个系统达到稳定均匀态时该控制器则自动关闭.

A class of intermittent feedback scheme is proposed to eliminate the spiral wave in the excitable media,which is described by the Fitz-Hugh-Nagumo equation.The activators of the sites is observed and compared with the selected threshold（less than the maximum activator）,a negative feedback is imposed on the whole system by inputting linear negative variable into the equation only when the sampled activator exceeds the threshold.It is found that the spiral wave is easier to be removed and the whole media becomes homogeneous when all the sites are monitored and smaller threshold is used,and the spiral wave just becomes sparse and breakup of spiral wave can be observed when the threshold is not small.On the other hand,weaker intensity of feedback still causes the spiral wave to be removed and the whole media still can become homogeneous when only one site is monitored.The controller will stop working as the whole media become homogeneous synchronically.