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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.

研究了Bonhoeffer-van der Pol(BVP)型反应扩散系统的时空分布。这项研究的动机是在脉冲碰撞的计算机模拟中意外观察到的特殊行为。也就是说，一对传播脉冲不会在碰撞时湮灭，而是构成持久地发射出射脉冲的磁区。这为我们提供了一个反例，即耗散系统中的脉冲在碰撞时简单地消失。我们称这种现象为自组织脉冲发生器。虽然BVP方程已经研究了二十多年，但这一性质尚未见报道。在我们的研究中，我们得到了以下事实。脉冲产生器的起源是双稳态，使得一致解和极限环共存。此外，系统的兴奋性和双稳性导致了各种时空图案。通过改变振荡强度和激发度参数，得到了相图。在二维中，目标图案由脉冲发生器形成。作为一个相关问题，我们还研究了具有一个激活剂和两个抑制剂的BVP型系统中的磁畴运动。与计算机模拟相关的界面动力学为我们提供了磁区的呼吸、摆动和混沌运动的条件。我们已经证明，摆动运动比呼吸运动出现在更宽的参数范围内。