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

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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.