论文标题
具有局部异质性的2-D Schnakenberg模型中的斑点模式
Spot Patterns in the 2-D Schnakenberg Model with Localized Heterogeneities
论文作者
论文摘要
开发了一种混合渐近学论理论,以分析不同类型的局部异质性对2组分Schnakenberg反应模型在2-D结构域中的局部斑点模式的存在,线性稳定性和缓慢动力学的影响。考虑了两种不同类型的局部异质性:在空间均匀的进料速率的强烈局部扰动以及去除域中一个小孔的效果,化学物质可以通过该孔泄漏出来。 Our hybrid theory reveals a wide range of novel phenomena such as, saddle-node bifurcations for quasi-equilibrium spot patterns that otherwise would not occur for a homogeneous medium, a new type of spot solution pinned at the concentration point of the feed rate, spot self-replication behavior leading to the creation of more than two new spots, and the existence of a creation-annihilation attractor with at most three spots.根据引入的局部异质性的类型,局部斑点被驱逐或吸引到渐近长时间尺度上的局部缺陷。通过广泛的完整PDE数值模拟,对慢速点动力学的结果和准平衡点模式的各种不稳定性进行了详细预测,所有这些结果都基于我们的混合渐近学学理论。
A hybrid asymptotic-numerical theory is developed to analyze the effect of different types of localized heterogeneities on the existence, linear stability, and slow dynamics of localized spot patterns for the two-component Schnakenberg reaction-diffusion model in a 2-D domain. Two distinct types of localized heterogeneities are considered: a strong localized perturbation of a spatially uniform feed rate and the effect of removing a small hole in the domain, through which the chemical species can leak out. Our hybrid theory reveals a wide range of novel phenomena such as, saddle-node bifurcations for quasi-equilibrium spot patterns that otherwise would not occur for a homogeneous medium, a new type of spot solution pinned at the concentration point of the feed rate, spot self-replication behavior leading to the creation of more than two new spots, and the existence of a creation-annihilation attractor with at most three spots. Depending on the type of localized heterogeneity introduced, localized spots are either repelled or attracted towards the localized defect on asymptotically long time scales. Results for slow spot dynamics and detailed predictions of various instabilities of quasi-equilibrium spot patterns, all based on our hybrid asymptotic-numerical theory, are illustrated and confirmed through extensive full PDE numerical simulations.