Robust balses in reaction-diffusion system

反应扩散系统中的稳健平衡

• 批准号: 08640480
• 负责人: OHTA Takao
• 金额: $ 1.47万
• 依托单位: Ochanomizu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640480/
• 关键词: reaction-diffusioin system; pulse; collision and breack up; pulse dynamics; bifurcation; pulse interaction; houlinear dissipative system; excitability; 界面方程式; 弾性的衝突; パルス方程式; 複素ギンツブルグランダウ方程式

We have carried out a theoretical analysis and computer simulations on the colision and break-up of pulses in a reaction diffusion system. The collision of pulses can be devided into two categories. One is an elastic-like collision. In this case, two pulses reverse their propagating direction at a finite distance without overlapping. This is called a hard collision. The other is that two pulses overlap each other at a collision, disappear temporally and survive again, which is called a soft collision. The latter is close to the soliton in an integrable system.Our theory of pulse dynamics is successful to clarify the mechanism of the hard collision. That is, the super critical bifurcation from a motionless to a propagating pulse is essential for this phenomenon. Just at postthershold, the velocity of a pulse is so small that the pulse cannot have a sufficient kinetic energy to overcome the potential barriar due to the repulsive nteraction. This fact also explains the reason as to why the elastic-like collision occurs only in a restricted parameter regime in the simulations.The soft collision which is more complicated is left for a future problem. A possible approach is to consider a perturbation of dissipative terms in an integrable limit. A formulation of an interplay between an ossilatory property and an excitable one in the collision process.

我们已经对反应扩散系统中脉冲的结构和破裂进行了理论分析和计算机模拟。脉冲的碰撞可以分为两类。一个是弹性状的碰撞。在这种情况下，两个脉冲在有限距离的情况下反转了它们的传播方向，而不会重叠。这被称为艰难的碰撞。另一个是两个脉冲在碰撞时相互重叠，暂时消失并再次生存，这称为软碰撞。后者在可集成的系统中靠近孤子。我们的脉冲动力学理论成功阐明了硬碰撞的机制。也就是说，从一动不动到传播脉冲的超临界分叉对于这种现象至关重要。就在后者后，脉冲的速度是如此之小，以至于脉冲无法具有足够的动能来克服由于排斥力而引起的潜在踪迹。这一事实还解释了为什么类似弹性的碰撞仅在模拟中的限制参数制度中发生的原因。更复杂的软碰撞留给了未来的问题。一种可能的方法是考虑在可集成限制的情况下考虑耗散术语的扰动。在碰撞过程中，渗透特性与令人兴奋的属性之间的相互作用的表述。

项目成果

T.Ohta他: "Collision of Proyagating Pulses in a Reaction-Piffusion System" J.Phys.Soc.Jpn. 66. 1551-1560 (1997)

T. Ohta 等人：“反应扩散系统中的前移脉冲的碰撞”J.Phys.Soc.Jpn. 66. 1551-1560 (1997)

T.Ohta and D.Jasnow: "Interface Dynamics for Layered Structures" Phys.Rev.E. 56. 6548-6558 (1997)

T.Ohta 和 D.Jasnow：“分层结构的界面动力学”Phys.Rev.E。

T.OHTA: "Collision of domain boundaries" Joural of Physical Society of Japan. 65・7. 1967-1970 (1996)

T.OHTA：“域边界的碰撞”日本物理学会杂志1967-1970（1996）。

T.Ohta他: "Spontaneous Formation of Concentric Waves in a R-D System" Phys.Rev.E. 54. 6074-6077 (1996)

T. Ohta 等人：“R-D 系统中同心波的自发形成”Phys.Rev.E 54. 6074-6077 (1996)

T.OHTA: "Spontaneous formation of concentric waves" Physical Review E. 54・6. 6074-6083 (1996)

T.OHTA：“同心波的自发形成”物理评论E.54・6083（1996）