具有空间平移模式的振荡对流的相位描述
Phase description of oscillatory convection with a spatially translational mode
摘要：
我们制定了一个理论的相位描述振荡对流在一个圆柱形的Hele-Shaw细胞是横向周期性的。该系统具有空间平移对称的横向方向，由于圆柱形以及时间平移对称。在这个系统中的振荡对流所描述的极限环的解决方案，具有两个相模式，一个是空间相，另一个是时间相。空间和时间相位分别指示对流的位置和振荡。本文所发展的理论可以被认为是无限维动力系统中极限环解的一种相位缩减方法，即，具有空间平移模式的振荡对流的偏微分方程的极限环解。我们推导出空间和时间相位的相位灵敏度函数;这些函数量化了振荡对流对每个空间点上施加的弱扰动的相位响应。利用相位灵敏度函数，我们刻画了振荡对流对弱空间激励的时空相位响应，并分析了弱耦合振荡对流系统之间的时空相位同步。
英文摘要：
We formulate a theory for the phase description of oscillatory convection in a cylindrical Hele-Shaw cell that is laterally periodic. This system possesses spatial translational symmetry in the lateral direction owing to the cylindrical shape as well as temporal translational symmetry. Oscillatory convection in this system is described by a limit-torus solution that possesses two phase modes; one is a spatial phase and the other is a temporal phase. The spatial and temporal phases indicate the position and oscillation of the convection, respectively. The theory developed in this paper can be considered as a phase reduction method for limit-torus solutions in infinite-dimensional dynamical systems, namely, limit-torus solutions to partial differential equations representing oscillatory convection with a spatially translational mode. We derive the phase sensitivity functions for spatial and temporal phases; these functions quantify the phase responses of the oscillatory convection to weak perturbations applied at each spatial point. Using the phase sensitivity functions, we characterize the spatiotemporal phase responses of oscillatory convection to weak spatial stimuli and analyze the spatiotemporal phase synchronization between weakly coupled systems of oscillatory convection.
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