Optique Nonlinéaire Théorique, Université Libre de Bruxelles (U.L.B.), CP 231, Belgium.
Phys Rev Lett. 2009 Oct 16;103(16):164501. doi: 10.1103/PhysRevLett.103.164501. Epub 2009 Oct 14.
We analytically study the influence of boundaries on distant localized patterns generated by a Turing instability. To this end, we use the Swift-Hohenberg model with arbitrary boundary conditions. We find that the bifurcation diagram of these localized structures generally involves four homoclinic snaking branches, rather than two for infinite or periodic domains. Second, steady localized patterns only exist at discrete locations, and only at the center of the domain if their size exceeds a critical value. Third, reducing the domain size increases the pinning range.
我们分析研究了边界对由 Turing 不稳定性产生的远程局域模式的影响。为此，我们使用具有任意边界条件的 Swift-Hohenberg 模型。我们发现，这些局域结构的分岔图通常涉及到四个同宿蛇形分支，而不是无限或周期域的两个。其次，如果它们的大小超过临界值，稳定的局域模式仅存在于离散位置，并且仅在域的中心存在。第三，减小域的尺寸会增加钉扎范围。
