Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification.
Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification.
复制标题
通过递归量化识别间歇信号动力学中的同宿轨道。
作者：
V. Nair;R. Sujith
在本文中，我们将展示如何在湍流流声相互作用系统中观察到的不稳定现象与相空间中同宿轨道的形成有关。通过平衡构型的稳定和不稳定流形的交叉出现的这种轨道是由与湍流对流和波传播相关的多个空间/时间尺度上发生的相互作用引起的。通过量化的时间所花费的动力学在非周期性的状态，使用递归图，我们展示了如何存在的同宿轨道的动力学可以令人信服地证明，这往往是不可能的，通过视觉检查的相空间的吸引子。
In this paper, we show how the phenomenon of intermittency observed in systems with turbulent flow-sound interaction is related to the formation of homoclinic orbits in the phase space. Such orbits that emerge via the intersection of the stable and unstable manifold of an equilibrium configuration result from interactions that happen at multiple spatial/temporal scales associated with turbulent convection and wave propagation. Through a quantification of the time spent by the dynamics in the aperiodic states using recurrence plots, we show how the presence of homoclinic orbits in the dynamics may be convincingly demonstrated, which is often not possible through a visual inspection of the phase space of the attractor.