Pattern Dynamics in an Excitable Reaction Diffusion System

本文在可激发反应扩散系统中获得了下列有关畴型动力学的新结果：1.为了研究半导体辉光放电和非线性电流中的畴型，我们引入了一个模型系统，它是一个激活剂和两个抑制剂的反应扩散方程的耦合组。该模型方程已被研究的计算机模拟和界面的方法。我们已经证明，激活剂的扩散常数足够小，而抑制剂之一具有极大的扩散系数。导出了一维界面运动方程，并进行了稳定性分析，得到了周期激励解的分岔图。通过数值模拟研究了阈值后的行为。通过改变参数，我们发现了复杂的区域运动，如倍周期运动、拟周期运动、呼吸运动和摆动运动等。2.通过计算机模拟具有一个激活剂和一个抑制剂的可激发反应扩散系统，得到了一致解与极限环振荡共存的新结果。当两个传播脉冲碰撞时，出现振荡域，并发出传出的波列。在二维空间中，我们观察到同心波的自动形成。从活化子的定域初始条件出发，我们得到了基本相同的结果。本文的结果与电流体动力对流中实验观察到的无起搏器的同心波定性一致。

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.