Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan.
Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan.
Phys Rev E. 2017 Oct;96(4-1):042203. doi: 10.1103/PhysRevE.96.042203. Epub 2017 Oct 9.
A positive Lyapunov exponent is the most convincing signature of chaos. However, existing methods for estimating the Lyapunov exponent from a time series often give unreliable estimates because they trace the time evolution of the distance between a pair of initially neighboring trajectories in phase space. Here, we propose a mathematical method for estimating the degree of dynamical instability, as a surrogate for the Lyapunov exponent, without tracing initially neighboring trajectories on the basis of the information entropy from a symbolic time series. We apply the proposed method to numerical time series generated by well-known chaotic systems and experimental time series and verify its validity.
正的 Lyapunov 指数是混沌最有说服力的特征。然而，从时间序列估计 Lyapunov 指数的现有方法通常给出不可靠的估计，因为它们追踪的是相空间中一对初始相邻轨迹之间的距离随时间的演化。在这里，我们提出了一种基于符号时间序列的信息熵来估计动力学不稳定性程度（作为 Lyapunov 指数的替代）的数学方法，而无需追踪初始相邻轨迹。我们将所提出的方法应用于由著名的混沌系统生成的数值时间序列和实验时间序列，并验证了其有效性。
