时变反应扩散系统中螺旋波和湍流的控制

研究了一类参数时变的反应扩散系统中螺旋波和湍流对外电场的响应问题.在数值模拟中，以一类改进的Fitzhugh-Nagumo模型为研究对象(在恰当参数值下可分别描述激发介质和振荡介质)，考虑随机和不确定因素(如内外噪声、气压、温度梯度分布和介质形变等)所引起的系统参数涨落对斑图演化的影响，在模拟中选取的参数涨落范围确保系统可以观测到稳定旋转的螺旋波、漫游的螺旋波和湍流，经历一定的暂态过程后，对介质施加极化电场，研究螺旋波和湍流在外电场中的演化.数值计算结果表明：在系统参数发生涨落和外电场强度比较小情况下，主关键词：螺旋波湍流时变系统Fitzhugh-Nagumo模型

Control of spiral wave and turbulence in the time-varied reaction-diffusion system

We investigated the external electric field-induced transition of the spiral wave and turbulence in a class of time-varied reaction-diffusion systems. In our numerical simulation, a modified Fitzhugh-Nagumo model, which was used to describe the excitable and/or oscillatory media under appropriate parameters, was investigated. The effect induced by the random and/or other uncertain factors (for example, external and interior noise, gas pressure, temperature gradient and deformation of media etc.) was considered. The amplitude of the fluctuations of parameters was selected at appropriate values so that stable rotating spiral wave, meandering spiral wave and turbulence could be observed respectively. The external electric field was introduced into the media after a transient period allowing for parameter fluctuations. It was found that only the breakup of spiral wave was observed and the whole media could not reach homogeneous state when weak electric field and parameter fluctuation were used. It was confirmed that the breakup of spiral wave happens and then the whole media becomes stably homogeneous when appropriately strong intensity of external electric field is applied to the whole media together with the action of parameter fluctuation. The snapshots of the activator are used to investigate the transition of the patterns in the presence of external electric field and under parameter fluctuation, and relevant theoretical discussion is given in the precent paper.