Robust balses in reaction-diffusion system

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。脉冲的碰撞可以分为两类。一种是弹性碰撞。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。这被称为硬碰撞。另一种是两个脉冲在碰撞时相互重叠，在时间上消失，然后再次存活，这称为软碰撞。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叉是这一现象的关键。就在热过后，脉冲的速度是如此之小，以至于脉冲不能有足够的动能来克服由于排斥相互作用而产生的势垒。这一事实也解释了为什么在模拟中只在受限参数区域发生弹性碰撞的原因。更复杂的软碰撞留给未来的问题来解决。一种可能的方法是考虑耗散项在可积极限中的摄动。在碰撞过程中，吸入性和可激动性之间相互作用的公式。

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.