Efficient and Accurate Methods for the Computation of Lyapunov Characteristic Exponents for n-Dimensional Continuous Dynamical Systems

n 维连续动力系统李雅普诺夫特征指数计算的高效准确方法

• 批准号: 0074151
• 负责人: Firdaus Udwadia
• 金额: $ 8万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0074151&HistoricalAwards=false
• 关键词: Efficient; Accurate; Methods; Computation; Lyapunov

Efficient and Accurate Methods for the Computation of Lyapunov Characteristic Exponents for n-Dimensional Dynamical SystemsAbstractThis proposal aims to develop computational methods for the efficient and accurate determination of the Lyapunov characteristic exponents of discrete and continuous dynamical systems. Since current methods are inadequate, our goal is to develop new computational techniques that can be used for general, n-dimensional systems. Thus, the development of new techniques for solving the variational equation of a system of nonlinear differential equations will be undertaken. The methods to be employed will be underpinned by mathematical analysis so that the algorithms developed will be both efficient and accurate. Several different methods will be investigated and compared with one another. Error analysis will be undertaken. Dissemination of the information will include the development of computer codes that are directly downloadable from the internet. The methods developed in this research effort will have applications in numerous areas of applied science and engineering. Nonlinear dynamics is a key feature in many structural systems, such as long span suspension bridges; in biomechanical systems, such as Central Pattern Generators for locomotion; and in the rapidly developing field of secure communication systems. Hence, the results of this research will have a considerable and direct impact on several real-life areas of application.

本文的目的是发展一种计算方法，用于有效和准确地确定离散和连续动力系统的李雅普诺夫特征指数。由于目前的方法是不够的，我们的目标是开发新的计算技术，可用于一般的，n维系统。因此，将发展新的技术来解决非线性微分方程系统的变分方程。所采用的方法将得到数学分析的支持，以便开发的算法既有效又准确。将研究几种不同的方法并相互比较。将进行误差分析。信息的传播将包括编制可直接从互联网下载的计算机代码。在这项研究工作中开发的方法将在应用科学和工程的许多领域中得到应用。非线性动力学是许多结构系统中的关键特征，例如大跨度悬索桥;在生物力学系统中，例如用于运动的中央模式发生器;以及在快速发展的安全通信系统领域中。因此，这项研究的结果将对几个实际应用领域产生相当大的直接影响。