Determining Lyapunov Exponents by Means of Interpolated Mapping

[+] Author and Article Information
Benson H. Tongue

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

David Smith

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

J. Appl. Mech 56(3), 691-696 (Sep 01, 1989) (6 pages) doi:10.1115/1.3176148 History: Received September 21, 1988; Revised December 22, 1988; Online July 21, 2009


The method of Interpolated Mapping is extended to encompass the calculation of transient system behavior, specifically the efficient determination of the Lyapunov exponents for a simple nonlinear system. Both the continuous Lyapunov exponents as well as the corresponding Lyapunov exponents of the Poincaré map for a forced Duffing’s oscillator are found. The use of Interpolated Mapping is compared to straightforward numerical integration and is shown to offer distinct computational advantages.

Copyright © 1989 by ASME
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