Lambda-Omega格点动力系统的稳定周期解
Stable Periodic Solutions to Lambda-Omega Lattice Dynamical Systems
摘要：
本文研究Lambda-Omega格点动力系统周期解的稳定性。特别是，我们表明，一个适当的animator铸造的晶格动力系统作为一个无限维的快慢微分方程。证明了在周期解的邻域内存在一个不变的慢流形，并且这个慢流形是一致指数吸引的。慢流形上的解的动力学变得更加复杂，需要更精细的处理。我们提出了充分条件，以保证收敛的慢流形是代数，而不是指数，在慢时间变量。特别感兴趣的是，我们的工作在这份手稿的旋转波解决方案的稳定性，最近发现存在于这里研究的Lambda-Omega系统。
英文摘要：
In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow differential equation. In a neighbourhood of the periodic solution an invariant slow manifold is proven to exist, and that this slow manifold is uniformly exponentially attracting. The dynamics of solutions on the slow manifold become significantly more complicated and require a more delicate treatment. We present sufficient conditions to guarantee convergence on the slow manifold which is algebraic, as opposed to exponential, in the slow-time variable. Of particular interest to our work in this manuscript is the stability of a rotating wave solution, recently found to exist in the Lambda-Omega systems studied herein.
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