Influence of the finite precision on the simulations of discrete dynamical systems

摘要

The effect of numerical precision on the mean distance and on the mean coalescence time between trajectories of two random maps was investigated. It was shown that mean coalescence time between trajectories can be used to characterize regions of the phase space of the maps. The mean coalescence time between trajectories scales as a power law as a function of the numerical precision of the calculations in the contracting and transitions regions of the maps. In the contracting regions the exponent of the power law is approximately one for both maps and it is approximately two in the transition regions for both maps. In the chaotic regions, the mean coalescence time between trajectories scales as an exponential law as a function of the numerical precision of the calculations for the maps. For both maps the exponents are of the same order of magnitude in the chaotic regions.