论文标题
关于混沌吸引子的起源，在五个BiharmonCoply耦合相振荡器的系统中，有两个零Lyapunov指数
On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators
论文作者
论文摘要
我们研究了四个微分方程的系统中的混沌动力学，该方程描述了与Biharmonic耦合的五个相同全球耦合相振荡器的动力学。我们表明，该系统在参数空间的广泛区域中显示了两个零（与数字中的零）lyapunov指数的奇怪的螺旋吸引子（Shilnikov吸引子）。我们通过对正在考虑的系统的三维庞加莱地图的分叉分析来解释这种现象。我们表明，当周期性轨道（Poincaré地图中的固定点）具有乘数的Triplet $（1，1，1）$时，混乱的动力学在这里发展。众所周知，这种分叉的渐近流正态形式与存在螺旋吸引子的三维Arneodo-Coullet-Spiegel-surster（ACST）系统相吻合。基于此，我们得出的结论是，观察到的吸引子中轨道的附加额定零lyapunov指数出现，因为相应的三维庞加莱地图与三维ACST-SYSTEM的时移图接近。
We study chaotic dynamics in a system of four differential equations describing the dynamics of five identical globally coupled phase oscillators with biharmonic coupling. We show that this system exhibits strange spiral attractors (Shilnikov attractors) with two zero (indistinguishable from zero in numerics) Lyapunov exponents in a wide region of the parameter space. We explain this phenomenon by means of bifurcation analysis of the three-dimensional Poincaré map for the system under consideration. We show that the chaotic dynamics develop here near a codimension three bifurcation, when a periodic orbit (fixed point in the Poincaré map) has the triplet $(1, 1, 1)$ of multipliers. As it is known, the asymptotic flow normal form for this bifurcation coincides with the three-dimensional Arneodo-Coullet-Spiegel-Tresser (ACST) system in which spiral attractors exist. Based on this, we conclude that the additional near-zero Lyapunov exponent for orbits in the observed attractors appear due to the fact that the corresponding three-dimensional Poincaré map is close to the time-shift map of the three-dimensional ACST-system.
