Determining Lyapunov Exponents by Means of Interpolated Mapping

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 Po...

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Bibliographic Details
Published in:Journal of applied mechanics 1989-09, Vol.56 (3), p.691-696
Main Authors: Tongue, Benson H, Smith, David
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Physics
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Summary: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 Poincare´ 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.
ISSN:0021-8936
1528-9036
DOI:10.1115/1.3176148