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 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.