论文标题
在多变量激活器抑制剂系统中排斥峰溶液的不稳定性机制
Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system
论文作者
论文摘要
我们研究了Meinhardt分支模型中亚临界图式分叉中生成的空间局部局部单峰状态和多峰状态的线性稳定性。在一个空间维度中，由于峰值排斥，这些状态是在叶的蛇形结构中组织的，但显示出所有线性不稳定的不稳定，而不稳定模式的数量随着存在的峰值而增加。尽管如此，在两个空间维度中，直接数值模拟揭示了稳定的单点和多点状态的存在，它们的性质取决于附近斑点的排斥以及域的形状以及所施加的边界条件。表现出前繁殖会触发新地点的增长，同时破坏他人的稳定。结果表明，多变量模型可以支持典型的两变量模型中不存在的新型行为。
We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a foliated snaking structure owing to peak-peak repulsion but are shown to be all linearly unstable, with the number of unstable modes increasing with the number of peaks present. Despite this, in two spatial dimensions direct numerical simulations reveal the presence of stable single- and multi-spot states whose properties depend on the repulsion from nearby spots as well as the shape of the domain and the boundary conditions imposed thereon. Front propagation is shown to trigger the growth of new spots while destabilizing others. The results indicate that multi-variable models may support new types of behavior that are absent from typical two-variable models.
