The reliable solution and computation time of variable parameters Logistic model

TL;DR

This paper investigates the reliable computation time of variable parameters logistic maps, providing methods to determine solution robustness and analyzing how it varies with initial conditions and parameters.

Contribution

It introduces a method to compute reliable solutions for VPLM and analyzes the distribution of reliable computation times across different initial values.

Findings

Mean Tc stabilizes with large sample sizes.

Maximum, minimum, and distribution of Tc are characterized.

Tc of fixed parameter logistic map matches theoretical predictions.

Abstract

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.