Self-Organized Pulse Generator in a Reaction-Diffusion System

反应扩散系统中的自组织脉冲发生器

基本信息

批准号：
06835007
负责人：
OHTA Takao
金额：
$ 1.34万
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：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

项目摘要

We have investigated the spatio-temporal pattern in a Bonhoeffer-van der Pol (BVP) type reaction- diffusion system. This study was motivated from the peculiar behavior observed unexpectedly in computer simulations of pulse collision. That is, a pair propagating pulses do not annihilate upon collision but constitute a domain which emits outgoing pulses persistently. This provides us with anti-example that pulses in a dissipative system simply disappear upon collision. We call this phenomenon a self-organized pulse generator. Although BVP equation had been studied for more than twenty years, the above property had not been reported.In our study, we have obtained the following facts. The origin of the pulse generator is the bistability such that a uniform solution and a limit cycle coexist. Furthermore, the excitability of the system and the bistability cause a variety of spatio-temporal patterns. The phase diagram is obtained by changing the parameters of oscillatory strength and excitability. In two dimensions, a target pattern is formed by the pulse generator. If one increases the diffusion constant, the target pattern becomes extended, localized and finally motionless.As a related problem, we have also studied domain motion in a BVP-type system with one activator and two inhibitors. The interface dynamics associated with computer simulations provides us with the condition of breathing, wiggling and chaotic motion of domains. We have shown that the wiggling motion appears in a wider parameter region than the breathing motion.

我们已经研究了Bonhoeffer-Van der Pol（BVP）型反应扩散系统中的时空模式。这项研究是从脉冲碰撞计算机模拟中意外观察到的特殊行为的动机。也就是说，一对传播脉冲不会在碰撞时消灭，而是构成一个持续发出的脉冲的域。这为我们提供了反示例，即耗散系统中的脉冲在碰撞时消失。我们称这种现象为自组织的脉冲发生器。尽管已经研究了BVP方程已有二十多年了，但尚未报告上述财产。在我们的研究中，我们获得了以下事实。脉冲发生器的起源是双态性，使得均匀的解和极限循环共存。此外，系统的兴奋性和双态性引起了多种时空模式。相图是通过更改振荡强度和兴奋性的参数获得的。在二维中，脉冲发生器形成目标模式。如果一个人增加了扩散常数，则目标模式会扩展，局部且最终不动。与计算机模拟相关的界面动力学为我们提供了域的呼吸，摇摆和混乱运动的状况。我们已经表明，摆动运动出现在更宽的参数区域中，而不是呼吸运动。