三维反应扩散系统中的螺旋波和失稳控制  

Spiral waves and instability control in 3D reaction-diffusion systems

作　　者：王宏利[1] 欧阳颀[1] 

机构地区：[1]北京大学物理学院,人工微结构和介观物理国家重点实验室,北京100871

出　　处：《中国科学：物理学、力学、天文学》2014年第12期1291-1300,共10页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家重点基础研究发展计划(编号:2007CB814802;2009CB918500);国家自然科学基金(批准号:10721403;11074009;11174013)资助项目

摘　　要：三维螺旋波(卷轴波)的运动和失稳的研究在心颤等高发心脏病中扮演重要角色,对三维螺旋波的运动和失稳过程以及控制的研究对于心颤等心脏病的防治具有指导意义.本文主要对我们过去几年在梯度系统中螺旋波的研究结果做一个总结.我们以反应扩散系统为研究对象,对于具有参数梯度的螺旋波的失稳过程和控制进行了探讨.在实验和数值模拟研究中,我们发现在三维梯度系统中,梯度大小的改变可以促使三维螺旋波发展产生线缺陷或者引起二维螺旋波运动的相位差的积累而产生漫游,两者都可使螺旋波的运动失去稳定性.对于螺旋波失稳的控制,我们研究了外力周期驱动和噪声对螺旋波失稳的影响,对控制的机制进行了分析.3D spiral waves or scroll waves as 3D analogs of 2D spiral waves have been expected to play an important role in heart diseases such as the ventricular fibrillation. The properties, instability and control approaches of scroll waves attracted persistent research interest in the past two decades. In this mini-review, we summarize the recent results we obtained regarding properties and control methods of scroll waves in reaction-diffusion systems with gradient in the third direction. It is demonstrated that appropriate gradient can not only induce line-defects on scroll waves in the region of excitability but also give rise to the accumulation of phase difference and induce meandering when the system is in the oscillatory regime. In both cases will cause instabilities and turbulence. As for the control of instabilities of scroll waves, we propose two scenarios, periodic driving and alternatively noise driving on the system in the vicinity of instabilities. Numerical and experimental results demonstrated that both approaches are effective provided the parameters be adjusted to appropriate values.

关 键 词：反应扩散 螺旋波 失稳 控制 

分 类 号：O231[理学—运筹学与控制论] R541[理学—数学]