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Estimation of Lyapunov Exponents Using a Semi-Discrete Formulation

[+] Author and Article Information
Josef S. Török

Department of Mechanical Engineering, Rochester Institute of Technology, Rochester NY 14623

Appl. Mech. Rev 46(11S), S229-S233 (Nov 01, 1993) doi:10.1115/1.3122641 History: Online April 29, 2009

Abstract

Lyaponov exponents are a generalization of the eigenvalues of a dynamical system at an equilibrium point. They are used to determine the stability of any type of steady-state behavior, including chaotic solutions. More specifically, Lyapunov exponents measure the exponential rates of divergence or convergence associated with nearby trajectories. This paper presents an efficient method of estimating the Lyapunov spectrum of continuous dynamical systems. Based on the Lie series expansion of the flow, the technique can be readily implemented to estimate the Lyapunov exponents of dynamical systems governed by ordinary differential equations.

Copyright © 1993 by American Society of Mechanical Engineers
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