标题： 双稳态离散晶格中局部态的蛇形和孤立结构 显示英文标题

标题： Snaking and isolas of localized states in bistable discrete lattices

摘要： 我们考虑离散双稳态Allen-Cahn方程中的局域状态。 这个模型方程以最简单的方式结合了双稳性和局部细胞间耦合。 稳定局域状态的存在是由于对底层格子的钉扎；它们在等效的连续方程中不存在。 特别是我们讨论分岔图中“孤立”解的存在：分岔图中解的闭合曲线。 在单个空间维度中，某些非周期性边界条件下会出现孤立，但在二维情况下似乎会普遍出现。 我们指出1D分岔图中的特征如何有助于解释2D分岔图中的一些（非直观的）特征。 显示英文摘要

摘要： We consider localized states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable localized states is made possible by pinning to the underlying lattice; they do not exist in the equivalent continuum equation. In particular we address the existence of 'isolas': closed curves of solutions in the bifurcation diagram. Isolas appear for some non-periodic boundary conditions in one spatial dimension but seem to appear generically in two dimensions. We point out how features of the bifurcation diagram in 1D help to explain some (unintuitive) features of the bifurcation diagram in 2D.