论文标题
耦合振荡器网络中的危险衰老过渡
Dangerous Aging Transition in a Network of Coupled Oscillators
论文作者
论文摘要
在本文中，我们研究了放松振荡器网络中的动态鲁棒性。特别是，我们考虑了一个扩散耦合的van der振荡器网络，以探索衰老的过渡现象。我们的研究表明，在范德尔振荡器网络中衰老过渡的机制与典型的正弦振荡器（如Stuart-Landau振荡器）完全不同。与正弦振荡器不同，顺序参数不遵循二阶相变。相反，由于临界点上突然的无界轨迹，我们观察到顺序参数的异常相变。我们称其为危险的衰老过渡。我们提供了这种异常相变的细节分叉分析。我们表明，极限循环振荡器的边界危机是这种危险的衰老过渡的掌舵者。
In this article, we investigate the dynamical robustness in a network of relaxation oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our investigation reveals that the mechanism of aging transition in a network of Van der Pol oscillator is quite different from that of typical sinusoidal oscillators such as Stuart-Landau oscillators. Unlike sinusoidal oscillators, the order parameter does not follow the second-order phase transition. Rather we observe an abnormal phase transition of the order parameter due to sudden unbounded trajectories at a critical point. We call it a dangerous aging transition. We provide details bifurcation analysis of such abnormal phase transition. We show that the boundary crisis of a limit-cycle oscillator is at the helm of such a dangerous aging transition.
