FitzHugh-Nagumo系统中螺旋波的控制

采用FitzHugh-Nagumo方程,研究了二维时空系统中螺旋波的控制问题,利用相空间压缩方法对部分系统变量的振幅进行限制从而影响螺旋波的稳定性.研究表明,控制过程可分为三个不同的阶段:在较小压缩限条件下螺旋波可以被完全消除,系统进入均匀定态;在较大的压缩限条件下螺旋波能够稳定存在,而且其振荡频率不随控制参数的改变而发生变化;当压缩限介于上述两者之间时,系统表现为时空混沌态.对上述控制过程进行了进一步的讨论,研究了不同控制参数条件下的系统斑图、变量的演化、相空间轨道等性质,并且对振幅函数和振荡频率特征进 关键词： 螺旋波 相空间压缩 FitzHugh-Nagumo方程

Control of spiral waves in FitzHugh-Nagumo systems

Control of spiral wave in two-dimensional FitzHugh-Nagumo equation is studied. The phase space compression approach is used to confine the system trajectory into a finite area and to annihilate spiral wave in the numerical simulation. Three stages are found in the control process. The spiral is driven to a homogenous stationary state when the compress limit is small; the spiral is stable with a fixed frequency when the compression limit is large; in the intermediate controlling parameter regime, the spatiotemporal turbulent state is observed. The controlling process is investigated by considering system pattern, variable evolution, phase space trajectory, etc, and the characteristics of amplitude function and oscillatory frequency are summarized as well.