标题： 确定性系统中的混沌检测与噪声 显示英文标题

标题： Testing for Chaos in Deterministic Systems with Noise

摘要： 最近，我们引入了一种新的测试方法，用于区分确定性动力系统中的规则和混沌动力学，并认为该测试在某些方面优于使用最大李雅普诺夫指数的传统混沌测试。 在本文中，我们研究了该测试处理中等数量噪声数据的能力。 将我们测试的改进版本与计算最大李雅普诺夫指数的“切空间”方法和“直接方法”进行了比较。 从逻辑斯蒂映射到一个八维微分方程的洛伦兹系统（洛伦兹96系统）的数值实验结果表明，我们的方法优于切空间方法，并且与直接方法相比具有明显优势。 显示英文摘要

摘要： Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent. In this paper, we investigate the capability of the test to cope with moderate amounts of noisy data. Comparisons are made between an improved version of our test and both the ``tangent space'' and ``direct method'' for computing the maximal Lyapunov exponent. The evidence of numerical experiments, ranging from the logistic map to an eight-dimensional Lorenz system of differential equations (the Lorenz 96 system), suggests that our method is superior to tangent space methods and that it compares very favourably with direct methods.