Pattern Dynamics in an Excitable Reaction Diffusion System

可兴奋反应扩散系统中的模式动力学

基本信息

批准号：
04640363
负责人：
OHTA Takao
金额：
$ 1.22万
依托单位：
Ochanomizu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1992
资助国家：
日本
起止时间：
1992 至 1993
项目状态：
已结题

项目摘要

We have obtained the following new results on pattern dynamics in an excitable reaction diffusion system.1.In order to investigate the domain pattern in glow discharge and in nonlinear electric current of semiconductors, we have introduced a model system which is a coupled set of reaction diffusion equations for one activator and two ingibitors. This model equations have been studied by computer simulations and by an interfacial approach. We have assumued that the diffusion constant of the activator is sufficiently small while one of the inhibitors has extremely large diffusivity. We have derived the interface equation of motion in one dimension and carried out the stability analysis to obtain the bifurcation diagram of periodic excited solutions. The behavior at post-threshold has been explored by numerical simulations. By changing the parameters, we have found complicated motions of domains such as period doubling and quasiperiodic motions as well as the breathing and wiggling motions.2.We have obtained novel results by computer simulations of an excitable reaction diffusion system with one activator and one inhibitor where a uniform solution coexists with a limit cycle oscillation. Upon a collision of two propagating pulses, an oscillatory domain emerges and it emitts outgoing wave trains. In two dimensions, we have observed an automatic formation of concentric waves. Starting with a localized initial condition of the activator, we have obtained essentially the same results. The present results are qualitatively consistent with the concentric waves without any pacemaker observed experimentally in electro-hydrodynamic convection.

我们已经在令人兴奋的反应扩散系统中获得了以下有关模式动力学的新结果。1。为了研究发光放电中的域模式和半导体的非线性电流中的域模式，我们引入了一个模型系统，该模型系统是一组耦合的反应扩散方程，用于一个激活剂和两个Ingibitor。该模型方程已通过计算机模拟和界面方法研究。我们假设激活剂的扩散常数足够小，而一种抑制剂的扩散率极高。我们在一个维度上得出了运动的界面方程，并进行了稳定分析以获得周期性激发溶液的分叉图。阈值后的行为已通过数值模拟探索。通过更改参数，我们发现了域的复杂动作，例如周期倍增和准碘动作以及呼吸和摇摆动作。2。我们通过计算机模拟了一种可激发反应扩散系统与一个激活剂和一个抑制剂解决方案的均匀解决方案与极限周期振荡共处的计算机模拟，从而获得了新的结果。两种繁殖脉冲发生碰撞后，出现了一个振荡域，并散发出波浪。在两个维度中，我们观察到同心波的自动形成。从激活剂的局部初始条件开始，我们获得了基本相同的结果。目前的结果与同心波在质量上是一致的，而没有任何在电 - 流动力对流实验中观察到的起搏器。