Mathematical Sciences: Stability and Dynamics of Parametrically Driven Waves

在这个项目中，主要研究者将研究 在许多物理系统中产生的波的结构 通过时间周期性驱动力的作用。 的 研究会从两个方向进行。 首先，首席研究员将研究如何 在激励系统中的时间驱动的影响通过以下方式来平衡： 空间对称性的影响。 这将需要使用一些 最近的方法分歧理论与对称性，以获得和 分析振幅方程。 其次，首席研究员将研究动态 大纵横比系统中的参数驱动波。 这种波表现出不同类型的不稳定性， 时空混沌 这种混乱的转变 行为将研究分析以及数字。

In this project the principal investigator will study the structure of waves that arise in a number of physical systems through the action of temporally periodic driving forces. The research will follow two directions. First of all, the principal investigator will study how the effect of temporal driving in exciting the system is balanced by the influence of spatial symmetries. This will entail using some recent methods of bifurcation theory with symmetry to derive and analyze the amplitude equations. Secondly, the principal investigator will study the dynamics of parametrically driven waves in large aspect-ratio systems. Such waves exhibit different types of instabilities that can lead to spatio-temporal chaos. The transitions to this chaotic behavior will be studied analytically as well as numerically.