论文标题
吸引子重建的统一和自动化方法
A unified and automated approach to attractor reconstruction
论文作者
论文摘要
我们提出了一种完全自动化的方法，用于从单变量和多变量时间序列进行最佳状态空间重建。提出的方法可以通过以共生方式统一两个有希望的想法来概括时间延迟嵌入过程。使用非均匀延迟允许成功地重建继承不同时间尺度的系统。与已建立的方法相反，适当的成本函数的最小化决定了嵌入维度，而无需使用阈值参数。此外，该方法能够检测随机时间序列，因此可以处理噪声污染的输入而无需调整参数。提出的方法的优越性显示在一些范式模型和混沌化学振荡器的实验数据上。
We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.
