关于可兴奋的β-骨架
On excitable beta-skeletons
摘要：
β-骨架是欧氏点集的平面邻近无向图，其中节点通过边连接，如果它们的基于lune的邻域不包含给定集合的其他点。参数$β$确定节点邻域的大小和形状。在一个可兴奋的β-骨架中，每个节点都有三种状态--休息、兴奋和不应，并根据其邻居的状态在离散时间内更新其状态。我们设计的β-骨架的绝对和相对阈值的兴奋性，并证明了几个不同的类的时空激发动力学可以选择使用β。这些类别包括螺旋波和目标波的激发，分支域的激发和振荡本地化。
英文摘要：
A beta-skeleton is a planar proximity undirected graph of an Euclidean point set where nodes are connected by an edge if their lune-based neighborhood contains no other points of the given set. Parameter $β$ determines size and shape of the nodes' neighborhoods. In an excitable beta-skeleton every node takes three states --- resting, excited and refractory, and updates its state in discrete time depending on states of its neighbors. We design families of beta-skeletons with absolute and relative thresholds of excitability and demonstrate that several distinct classes of space-time excitation dynamics can be selected using beta. The classes include spiral and target waves of excitation, branching domains of excitation and oscillating localizations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
