Lyap: A fortran 90 program to compute the Lyapunov exponents of a dynamical system from a time series

Abstract
The program presented computes all the Lyapunov exponents of an unknown dynamical system from a time series. The method used is based on a fitting of the time series with an analytical function through a least square minimization, after which the Lyapunov exponents are determined from the stability of the trajectories calculated using this analytical function.

Title of program: LYAP
Catalogue Id: ADHC_v1_0

Nature of problem
The program calculates all the Lyapunov exponents of a dynamical system when the law of evolution is unknown, as is the case for most of the systems studied in applied science (astronomy, biology, ...), and only a set of data in the form of a time series is available.

Versions of this program held in the CPC repository in Mendeley Data
ADHC_v1_0; LYAP; 10.1016/S0010-4655(97)00124-0

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本程序可基于时间序列，求解未知动力学系统的全部李雅普诺夫指数（Lyapunov exponents）。所采用的方法通过最小二乘极小化将时间序列拟合为解析函数，随后基于该解析函数计算得到的轨迹稳定性，确定李雅普诺夫指数。

程序名称：LYAP
目录编号：ADHC_v1_0

问题描述
当动力学系统的演化规律未知时，这也是应用科学研究中多数系统的典型研究场景（如天文学、生物学等），本程序可计算该系统的全部李雅普诺夫指数，此时仅可获取一组时间序列形式的数据集。

Mendeley数据的CPC资料库中收录的本程序版本：ADHC_v1_0；LYAP；10.1016/S0010-4655(97)00124-0

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2019）