Mt. White et Bh. Tongue, APPLICATION OF INTERPOLATED CELL MAPPING TO AN ANALYSIS OF THE LORENZEQUATIONS, Journal of sound and vibration, 188(2), 1995, pp. 209-226
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.