  The reliable computation time (RCT, marked as Tc) when applying a double
precision computation of a variable parameters logistic map (VPLM) is studied.
First, using the method proposed, the reliable solutions for the logistic map
are obtained. Second, for a time-dependent non-stationary parameters VPLM,
10000 samples of reliable experiments are constructed, and the mean Tc is then
computed. The results indicate that for each different initial value, the Tcs
of the VPLM are generally different. However, the mean Tc trends to a constant
value once the sample number is large enough. The maximum, minimum and probable
distribution function of Tc is also obtained, which can help us to identify the
robustness of applying a nonlinear time series theory to forecasting while
using the VPLM output. In addition, the Tc of the fixed parameter experiments
of the logistic map was obtained, and the results suggested that this Tc
matches the theoretical formula predicted value.
