On obtaining global nonlinear system characteristics through interpolated cell mapping

Abstract Period doubling bifurcations and fractal basin boundaries are investigated by means of Interpolated Cell Mapping (ICM). ICM is a new method to determine the continuous time trajectory of a nonlinear system by spatially discretizing the system and employing an interpolation procedure to estimate the system's response at any arbitrary point in phase space. The parameter values at which period doubling occurs for a Duffing's oscillator is found by both conventional time integration and two mapping techniques and the results compared. The ICM method is shown to very accurately determine the points of bifurcation. The dimension of a fractal basin boundary is determined by ICM and compared to an exact determination. The ICM procedure produces the same fractal dimension determination as the exact analysis but only requires one thousandth of the computation time.