APPLICATION OF INTERPOLATED CELL MAPPING TO AN ANALYSIS OF THE LORENZEQUATIONS

The Lyapunov exponents of the Lorenz equations are calculated using in terpolated cell mapping. The effects of mapping time step and cell siz e on accuracy and computation time are analyzed, leading to the identi fication of optimal cell size and time step values. A higher order int erpolation method for interpolated cell mapping is described. The accu racy and computation time of this method are compared to numerical int egration for calculating the basins of attraction of the Lorenz equati ons and the dimension of the basin boundaries. Regions of state space with high levels of deformation are shown to exist where the basin bou ndaries are most dense. (C) 1995 Academic Press Limited.