The reliable solution and computation time of variable parameters logistic model

The study investigates the reliable computation time (RCT, termed as Tc) by applying a double-precision computation of a variable parameters logistic map (VPLM). Firstly, by using the proposed method, we obtain the reliable solutions for the logistic map. Secondly, we construct 10,000 samples of reliable experiments from a time-dependent non-stationary parameters VPLM and then calculate the mean Tc. 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 when the sample number is large enough. The maximum, minimum, and probable distribution functions of Tc are also obtained, which can help us to identify the robustness of applying a nonlinear time series theory to forecasting by using the VPLM output. In addition, the Tc of the fixed parameter experiments of the logistic map is obtained, and the results suggest that this Tc matches the theoretical formula-predicted value.