Attractor radius for fractional Lorenz systems and their application to the quantification of predictability limits.
Attractor radius for fractional Lorenz systems and their application to the quantification of predictability limits.
复制标题
DOI：
10.1063/5.0113709
复制
发表时间：
2023-01
期刊：
影响因子：
2.9
通讯作者：
Yejuan Wang;Zhiqiang Wei;Guolin Feng
中科院分区：
文献类型：
--
作者：
Yejuan Wang;Zhiqiang Wei;Guolin Feng
量化混沌系统及其预测模型的可预测性极限已经引起了科学家们的极大兴趣。吸引子半径（AR）和全局吸引子半径（GAR）作为混沌系统的内在属性，在最近的工作中被引入（Li et al. 2018）。与传统的误差饱和或渐近值相比，AR和GAR提供了更准确、更客观的指标来评估预测模型的全局和局部可预报性极限。在这项工作中，我们考虑分数洛伦兹系统的AR和GAR，介绍了在Grigorenko和Grigorenko [Phys. Rev. Lett. 91，034101（2003）]使用Caputo分数导数及其对可预测性极限的量化的应用。一个惊人的发现是，分数Lorenz系统具有较小的吸引子半径和较短的可预测性极限，其中较小的吸引子是所有相关相等导数的阶数之和。此外，我们提出了一种新的数值算法的分数Lorenz系统，这是标准的四阶Runge-Kutta格式的推广版本。
Quantifying the predictability limits of chaotic systems and their forecast models has attracted much interest among scientists. The attractor radius (AR) and the global attractor radius (GAR), as intrinsic properties of a chaotic system, were introduced in the most recent work (Li et al. 2018). It has been shown that both the AR and GAR provide more accurate, objective metrics to access the global and local predictability limits of forecast models compared with the traditional error saturation or the asymptotic value. In this work, we consider the AR and GAR of fractional Lorenz systems, introduced in Grigorenko and Grigorenko [Phys. Rev. Lett. 91, 034101 (2003)] using the Caputo fractional derivatives and their application to the quantification of the predictability limits. A striking finding is that a fractional Lorenz system with smaller Σ, which is a sum of the orders of all involved equal derivatives, has smaller attractor radius and shorter predictability limits. In addition, we present a new numerical algorithm for the fractional Lorenz system, which is the generalized version of the standard fourth-order Runge-Kutta scheme.