Measuring transient chaos in nonlinear one- and two-dimensional maps

In this paper, we present results of numerical experiments on chaotic transients in families of the logistic and Hénon maps. The duration of chaotic transients (the rambling time) for logistic maps estimated according to a rigorous criterion shows monotonic regularities with respect to both the period and the number of periodic window in a series of a given period. Due to inapplicability of this criterion to multidimensional maps, a more universal, though approximate, criterion is systematically studied on the family of logistic maps to optimize a choice of the free parameter value. The same approximate criterion is used to estimate rambling time for a number of periodic windows for the family of Hénon maps. The dependence of the rambling time on the width of periodic windows is tested.