三组分反应扩散系统脉冲动力学的匹配渐近展开方法
Matched asymptotic expansion approach to pulse dynamics for a three-component reaction diffusion systems
摘要：
研究了一类具有一个活化剂和两个抑制剂的奇摄动三组分反应扩散方程组脉冲驻波解的存在性和稳定性。利用匹配渐近展开方法构造解，利用奇异极限本征值问题方法研究其稳定性.这种方法不仅是几何奇异扰动和Evans函数的另一种方法，而且具有两个优点：一是可以推广到高维情形，二是可以获得关于临界特征值行为的更精确的信息.这意味着存在余维两个奇异性的漂移和Hopf分岔的驻脉冲解决方案，它是数值证实，稳定的常设和旅行呼吸出现周围的奇异性在物理上可接受的制度。
英文摘要：
We study the existence and stability of standing pulse solutions to a singularly perturbed three-component reaction diffusion system with one-activator and two-inhibitor type. We apply the MAE (matched asymptotic expansion) method to the construction of solutions and the SLEP (Singular Limit Eigenvalue Problem) method to their stability properties. This approach is not just an alternative approach to geometric singular perturbation and the associated Evans function, but gives us two advantages: one is the extendability to higher dimensional case, and the other is to allow us to obtain more precise information on the behaviors of critical eigenvalues. This implies the existence of codimension two singularity of drift and Hopf bifurcations for the standing pulse solution and it is numerically confirmed that stable standing and traveling breathers emerge around the singularity in a physically-acceptable regime.
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