论文标题
使用扩展的动态模式分解评估更高维双曲系统的景点区域
Evaluation of the Region of Attractions of Higher Dimensional Hyperbolic Systems using the Extended Dynamic Mode Decomposition
论文作者
论文摘要
本文提出了一种原始方法，以使用通过扩展动态模式分解算法给出的Koopman操作员的离散时间近似的特征函数来计算双曲和多项式非线性动力学系统中吸引区域。提出的方法依赖于Koopman操作员的光谱分解来构建捕获吸引区域边界的本征函数。该算法仅依赖于可以在实验研究中收集的数据，并且不需要系统的数学模型。动态系统的两个示例，一个人群模型和更高的尺寸化学反应系统，允许证明结果的可靠性。
This paper proposes an original methodology to compute the regions of attraction in hyperbolic and polynomial nonlinear dynamical systems using the eigenfunctions of the discrete-time approximation of the Koopman operator given by the extended dynamic mode decomposition algorithm. The proposed method relies on the spectral decomposition of the Koopman operator to build eigenfunctions that capture the boundary of the region of attraction. The algorithm relies solely on data that can be collected in experimental studies and does not require a mathematical model of the system. Two examples of dynamical systems, a population model and a higher dimensional chemical reaction system, allows demonstrating the reliability of the results.
