论文标题
金茨堡的模式选择性反馈稳定 - landau螺旋波
Pattern-Selective Feedback Stabilization of Ginzburg--Landau Spiral Waves
论文作者
论文摘要
Ginzburg-landau方程式是图案形成的范式，以及Ginzburg的存在和稳定性 - Landau $ m $ m $ m $臂的螺旋波已被广泛研究。但是，许多多臂螺旋波不稳定，因此在实验和数值模拟中很少看到。在本文中，我们选择性地稳定了圆形和球形几何形状内某些重要类别的不稳定螺旋波。结果，首次获得具有任意臂数的稳定螺旋波。我们的稳定工具是对称性控制三重方法，这是对Pyragas控制对PDES设置的广泛应用的概括。
The complex Ginzburg--Landau equation serves as a paradigm of pattern formation and the existence and stability properties of Ginzburg--Landau $m$-armed spiral waves have been investigated extensively. However, many multi-armed spiral waves are unstable and thereby rarely visible in experiments and numerical simulations. In this article we selectively stabilize certain significant classes of unstable spiral waves within circular and spherical geometries. As a result, stable spiral waves with an arbitrary number of arms are obtained for the first time. Our tool for stabilization is the symmetry-breaking control triple method, which is an equivariant generalization of the widely applied Pyragas control to the setting of PDEs.
