时空混沌对可激发介质中螺旋波的影响的研究

THE STUDY ON THE EFFECT OF SPATIOTEMPORAL CHAOS ON SPIRAL WAVES IN EXCITABLE MEDIA

心肌细胞里离子通道的随机打开,在心肌组织中产生的空间分布电流就是时空混沌的.为了了解时空混沌对螺旋波的影响,基于B(a|¨)r模型研究了两层耦合可激发介质系统中螺旋波的演化,提出无条件和有条件两种驱动响应耦合.耦合前,驱动和响应子系统分别处于时空混沌态和螺旋波态.在不同的参数下,发现螺旋波表现出不同的动力学行为.在很小的耦合强度下,时空混沌对螺旋波动力学行为几乎无影响.当耦合强度很大时,无条件耦合总是导致螺旋波的破碎.当相关参数适当选取时,时空混沌既能提高受其作用介质的激发性,也能降低它的激发性.此外,它还能使稳定螺旋波和漫游螺旋波作无规漫游或无规漂移,甚至导致螺旋波漂移出系统;对于不稳定螺旋波,时空混沌能极大延迟螺旋波出现破碎.特别是,在有条件耦合下,可以使不稳定螺旋波成为稳定或漫游螺旋波.

The stochastic opening of ion channel in myocardial cells can generate spatially dis- tributed currents in cardiac tissue. These currents are spatiotemporal chaos. In order to know the effect of spatiotemporal chaos on spiral wave, we investigate the evolution of spiral waves in a system of two coupled excitable media by using BAEr model. The drive-response coupling schemes with or without constraint condition are proposed. The response and drive subsystems are respectively in the state of spiral wave and spatiotemporal chaos before the coupling turns on. We find that spiral wave exhibits different dynamical behaviors for dif- ferent parameters. When the coupling strength is weak, the dynamical behavior of spiral wave in response system almost remains unchanged. When the coupling strength is strong, the coupling without constraint condition always leads to the breakup of spiral wave. When the related parameters are properly chosen, spatiotemporal chaos not only can enhance the excitation of the forced medium but also reduce it. In addition, it can induce chaotic mean- der or drift of a stable or meandering spiral wave, and even causes spiral wave to move out of system. It can greatly delay the breakup of an unstable spiral wave. Specially, it causes an unstable spiral wave become a stable or chaotically meandering spiral wave under the coupling with constraint condition.