Abstract 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 neighborhood 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.

中文翻译：

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Lambda-Omega 晶格动力学系统的稳定周期解

摘要 在这篇手稿中，我们考虑了 Lambda-Omega 晶格动力学系统周期解的稳定性。特别是，我们表明适当的 ansatz 将晶格动力学系统转换为无限维快慢微分方程。在周期解的邻域中，一个不变的慢流形被证明存在，并且这个慢流形是均匀指数吸引的。慢流形上的溶液动力学变得更加复杂，需要更精细的处理。我们提出了足够的条件来保证在慢时间变量中的慢流形上收敛，该流形是代数的，而不是指数的。我们在这份手稿中的工作特别感兴趣的是旋转波解的稳定性，