Institut für Mathematik I, Free Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany.
Philos Trans A Math Phys Eng Sci. 2010 Jan 28;368(1911):319-41. doi: 10.1098/rsta.2009.0232.
We study diffusively coupled oscillators in Hopf normal form. By introducing a non-invasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super- and subcritical cases, we state a condition on the oscillator's nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of odd-number orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.
我们研究了 Hopf 正规形式下的扩散耦合振荡器。通过引入非侵入式延迟耦合，我们能够稳定固有不稳定的反相轨道。对于超临界和亚临界情况，我们给出了一个关于振荡器非线性的条件，这个条件是成功稳定所需的充分必要条件。我们证明了这些条件，并回顾了以前通过时滞反馈稳定奇数轨道的结果。最后，我们用数值模拟来说明这些结果。
