论文标题
在扰动的雷利 - 纳德对流中的周期性轨道的共鸣，对称性和分叉
Resonance, symmetry, and bifurcation of periodic orbits in perturbed Rayleigh-Bénard convection
论文作者
论文摘要
本文研究了雷利 - 纳德对流中出现的周期性轨道的全球结构，该结构是通过二维扰动的哈密顿模型模拟的，该结构通过着重于周期轨道的共鸣，对称性和分叉来建模。首先，我们通过数值检测Poincaré部分的相关周期点来显示扩展相空间中周期轨道的全局结构。然后，我们说明了如何出现共振的周期性轨道，并明确澄清了这种共振周期轨道的某些对称属性，这些轨道投射在相空间上；也就是说，当相对于单元格的水平和垂直中心线对称时，$ m $和绕组数$ n $就会变得奇怪。此外，当扰动的幅度$ \ varepsilon $变化时，描绘了周期性轨道分叉的全局结构，因为在实验中，当对流的振荡幅度逐渐增加时，当瑞利数量升高时，对流的振荡幅度会逐渐增加。
This paper investigates the global structures of periodic orbits that appear in Rayleigh-Bénard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the periodic orbits. First, we show the global structures of periodic orbits in the extended phase space by numerically detecting the associated periodic points on the Poincaré section. Then, we illustrate how resonant periodic orbits appear and specifically clarify that there exist some symmetric properties of such resonant periodic orbits which are projected on the phase space; namely, the period $m$ and the winding number $n$ become odd when an $m$-periodic orbit is symmetric with respect to the horizontal and vertical center lines of a cell. Furthermore, the global structures of bifurcations of periodic orbits are depicted when the amplitude $\varepsilon$ of the perturbation is varied, since in experiments the amplitude of the oscillation of the convection gradually increases when the Rayleigh number is raised.
