A modified interpolated cell mapping method

Abstract

A modified interpolated cell mapping (MICM) method is developed for global analysis of deterministic dynamical systems with smooth basin boundaries. By improving the algorithm of the interpolated cell mapping (ICM) and including the idea of sampling mappings of cells from the generalized cell mapping (GCM), MICM gives a more complete and precise global analysis of systems than ICM. In addition, based on analysis using MICM, a method using exact mappings is proposed to remedy the inaccuracy and incompleteness of global analysis due to interpolated mappings and the assumption of the sink cell. For the three systems studied in this paper, this method locates identical attractors and basins of attraction as the integration of a grid of points (IGP) method, with a 100-fold improvement in computational efficiency. (C) 1997 Academic Press Limited.