Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, 14195 Berlin, Germany.
Philos Trans A Math Phys Eng Sci. 2013 Aug 19;371(1999):20120472. doi: 10.1098/rsta.2012.0472. Print 2013 Sep 28.
The modest aim of this case study is the non-invasive and pattern-selective stabilization of discrete rotating waves ('ponies on a merry-go-round') in a triangle of diffusively coupled Stuart-Landau oscillators. We work in a setting of symmetry-breaking equivariant Hopf bifurcation. Stabilization is achieved by delayed feedback control of Pyragas type, adapted to the selected spatio-temporal symmetry pattern. Pyragas controllability depends on the parameters for the diffusion coupling, the complex control amplitude and phase, the uncontrolled super-/sub-criticality of the individual oscillators and their soft/hard spring characteristics. We mathematically derive explicit conditions for Pyragas control to succeed.
本案例研究的目标较为有限，旨在通过延迟反馈控制（Pyragas 型）对三角型扩散耦合 Stuart-Landau 振子中离散旋转波（“旋转木马上的小马”）进行非侵入式、模式选择性的稳定化，这种反馈控制适用于所选的时空对称模式。我们在对称破缺的等变 Hopf 分岔环境中进行工作。Pyragas 可控性取决于扩散耦合参数、控制幅度和相位的复数值、单个振子的超/亚临界性以及它们的软/硬弹簧特性。我们从数学上推导出了 Pyragas 控制成功的显式条件。
