论文标题
平面双晶格中的局部模式弱耦合晶格系统
Localized patterns in planar bistable weakly coupled lattice systems
论文作者
论文摘要
已知存在于错综复杂的分叉图中存在的空间扩展的Bistable系统中的局部平面模式，通常称为蛇曲线。他们的分析是具有挑战性的，因为该技术诸如空间动力学之类的技术，这些技术被用来解释一个空间维度在平面案例中不再起作用。在这里，我们考虑在方形晶格上摆放的双态系统，并使用Lyapunov--Schmidt还原提供了在抗胞菌限制附近的蛇的分析说明。我们还为局部模式建立了稳定性结果，讨论对不对称状态的分叉，并提供了进一步的数值证据，表明蛇曲线的形状随着反映空间耦合强度的系数跨越有限阈值而发生的。
Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their analysis is challenging as techniques such as spatial dynamics that have been used to explain snaking in one space dimension no longer work in the planar case. Here, we consider bistable systems posed on square lattices and provide an analytical explanation of snaking near the anti-continuum limit using Lyapunov--Schmidt reduction. We also establish stability results for localized patterns, discuss bifurcations to asymmetric states, and provide further numerical evidence that the shape of snaking curves changes drastically as the coefficient that reflects the strength of the spatial coupling crosses a finite threshold.
