关于几乎周期解的存在性及其在全局同步中的应用
On the Existence of Almost Periodic Solutions with Applications to Global Entrainment
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中文总结 AI 辅助
研究给定动力系统几乎周期解的存在性与稳定性，通过局部指数稳定性和输入到状态稳定性等方法，证明其可保证对小几乎周期输入的全局同步，并应用于Lotka - Volterra系统，结果可扩展到一致递归情形。
中文摘要 AI 辅助
本文给出了两个结果，对研究给定动力系统中几乎周期解的存在性和稳定性性质有用。所得结果是周期系统近期结果的推广，并应用于非线性时不变控制系统的全局同步问题。表明无外力系统的局部指数稳定性和相对于小输入的输入到状态稳定性可保证对小几乎周期输入的全局同步。以此方式，在具有Volterra - Lyapunov稳定相互作用矩阵的Lotka - Volterra系统中证明了全局同步。所有结果可扩展到一致递归情形。
英文摘要
This paper provides two results that are useful in the study of the existence and the stability properties of almost periodic solutions for a given dynamical system. The obtained results are generalizations of recent results for periodic systems and are applied to the global entrainment problem in nonlinear time-invariant control systems. It is shown that local exponential stability for the unforced system and input-to-state stability with respect to small inputs can guarantee global entrainment to small almost periodic inputs. In this way, global entrainment is shown in Lotka-Volterra systems with a Volterra-Lyapunov stable interaction matrix. All results can be extended to the uniformly recurrent case.
