标题： 一个湍流吸引子内的层流混沌马鞍 显示英文标题

标题： A laminar chaotic saddle within a turbulent attractor

摘要： 在具有高维混沌吸引子的系统中，如流体湍流，经常观察到弱混沌（层流）状态和强混沌（爆发）状态之间的间歇性切换。它们与低维系统中的间歇性不同，后者伴随着固定点或周期轨道的稳定性变化，而高维系统的间歇性倾向于在广泛的参数范围内出现。本文考虑了一种情况，其中层流状态的骨架$L$作为混沌吸引子$X$的一个适当混沌子集$S$存在，即$S\ \subsetneq\ X$。我们通过一个混沌鞍$S$来表征这种层流状态$L$，该混沌鞍被不同不稳定方向的周期轨道密集填充。这项研究证明了在流体湍流和相位同步中存在底层的混沌鞍。此外，我们确认混沌鞍在广泛的参数范围内持续存在。而且，一种类型的相位同步在湍流模型中被发现发生。 显示英文摘要

摘要： Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a low-dimensional system accompanied by the stability change of a fixed point or a periodic orbit in that the intermittency of a high-dimensional system tends to appear in a wide range of parameters. This paper considers a case where the skeleton of a laminar state $L$ exists as a proper chaotic subset $S$ of a chaotic attractor $X$, that is, $S\ \subsetneq\ X$. We characterize such a laminar state $L$ by a chaotic saddle $S$, which is densely filled with periodic orbits of different numbers of unstable directions. This study demonstrates the presence of chaotic saddles underlying intermittency in fluid turbulence and phase synchronization. Furthermore, we confirm that chaotic saddles persist for a wide range of parameters. Also, a kind of phase synchronization turns out to occur in the turbulent model.