论文标题
大幅度径向对称点和旱地生态系统模型中的差距
Large amplitude radially symmetric spots and gaps in a dryland ecosystem model
论文作者
论文摘要
我们使用空间动力学和几何学动力学和几何奇异扰动理论，在平坦的植被模式形成的两个组成式旱地生态系统模型中构建了远距离发作的径向对称斑点和间隙溶液。我们在相同型号中与旅行和固定前解决方案的几何形状与间隙解决方案之间的几何形状进行了连接。特别是，我们通过得出与该点相关的关键特征值与编码附近固定前部侧带不稳定的系数之间的渐近特征值之间的渐近关系，证明了较大半径的不稳定。此外，我们证明斑点不稳定与角方向上中间波长的一系列扰动，前提是斑点半径不太小。我们的结果伴随着数值模拟和光谱计算。
We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dynamics and geometric singular perturbation theory. We draw connections between the geometry of the spot and gap solutions with that of traveling and stationary front solutions in the same model. In particular, we demonstrate the instability of spots of large radius by deriving an asymptotic relationship between a critical eigenvalue associated with the spot and a coefficient which encodes the sideband instability of a nearby stationary front. Furthermore, we demonstrate that spots are unstable to a range of perturbations of intermediate wavelength in the angular direction, provided the spot radius is not too small. Our results are accompanied by numerical simulations and spectral computations.
