Title: Arbitrarily weak head-on collision can induce annihilation -- The role of hidden instabilities Show Chinese title

Title: 任意微弱的正面对撞可以引发湮灭——隐藏不稳定性的作用

Abstract: In this paper, we focus on annihilation dynamics for the head-on collision of traveling patterns. A representative and well-known example of annihilation is the one observed for 1-dimensional traveling pulses of the FitzHugh-Nagumo equations. In this paper, we present a new and completely different type of annihilation arising in a class of three-component reaction diffusion system. It is even counterintuitive in the sense that the two traveling spots or pulses come together very slowly but do not merge, keeping some separation, and then they start to repel each other for a certain time. Finally, up and down oscillatory instability emerges and grows enough for patterns to become extinct eventually (see Figs. 1-3). There is a kind of hidden instability embedded in the traveling patterns, which causes the above annihilation dynamics. The hidden instability here turns out to be a codimension 2 singularity consisting of drift and Hopf (DH) instabilities, and there is a parameter regime emanating from the codimension 2 point in which a new type of annihilation is observed. The above scenario can be proved analytically up to the onset of annihilation by reducing it to a finite-dimensional system. Transition from preservation to annihilation is also discussed in this framework. Show Chinese abstract

Abstract: 在本文中，我们关注行波模式正面对撞的湮灭动力学。 湮灭的一个典型且著名的例子是FitzHugh-Nagumo方程的一维行波脉冲中观察到的现象。 在本文中，我们提出了一类三组分反应扩散系统中出现的一种新型且完全不同的湮灭类型。 这种现象甚至有些反直觉，因为两个行波斑点或脉冲缓慢地靠近但不会合并，保持一定的距离，然后它们开始相互排斥一段时间。 最终，上下振荡不稳定性出现并增长，使模式最终消失（见图1-3）。 行波模式中存在一种隐藏的不稳定性，导致上述湮灭动力学。 这里的隐藏不稳定性被证明是一种由漂移和霍普夫（DH）不稳定性组成的双临界奇点，并且存在一个从双临界点出发的参数区域，在该区域内观察到了一种新型的湮灭。 上述情景可以通过将其简化为有限维系统来分析性地证明，直到湮灭的发生。 在此框架下，还讨论了从保存到湮灭的转变。