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.

我们对反应扩散系统中脉冲的碰撞和分裂进行了理论分析和计算机模拟。脉冲碰撞可以分为两类。一种是类弹性碰撞。在这种情况下，两个脉冲在有限距离内反转其传播方向而不重叠。这称为硬碰撞。另一种是两个脉冲在碰撞时相互重叠，暂时消失并再次存活，这称为软碰撞。后者接近于可积系统中的孤子。我们的脉冲动力学理论成功地阐明了硬碰撞的机制。也就是说，从静止脉冲到传播脉冲的超临界分岔对于这种现象至关重要。就在后阈值处，脉冲的速度非常小，以至于由于排斥相互作用，脉冲无法具有足够的动能来克服势垒。这一事实也解释了为什么模拟中类弹性碰撞仅发生在受限参数范围内的原因。更复杂的软碰撞留待将来解决。一种可能的方法是考虑可积极限内耗散项的扰动。碰撞过程中振荡特性和可兴奋特性之间相互作用的一种表述。