Abstract
The study investigates the reliable computation time (RCT, termed as T c) 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 T c. The results indicate that, for each different initial value, the T cs of the VPLM are generally different. However, the mean T c trends to a constant value when the sample number is large enough. The maximum, minimum, and probable distribution functions of T c 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 T c of the fixed parameter experiments of the logistic map is obtained, and the results suggest that this T c matches the theoretical formula-predicted value.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brent RP (1978) A Fortran multiple-precision arithmetic package. ACM Trans Math Softw 4(1):57–70
Liu Y, Wang PF, Huang G (2015) Study on the reliable computation time of the numerical model using the sliding temporal correlation method. Theor Appl Climatol 119:539–550
May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261(5560):459–467
Oteo JA, Ros J (2007) Double precision errors in the logistic map: statistical study and dynamical interpretation. Phys Rev E 76(3):036214
Oyanarte P (1990) MP—a multiple precision package. Comput Phys Commun 59(2):345–358
Wang PF, Li JP (2014) On the relation between reliable computation time, float-point precision and the Lyapunov exponent in chaotic systems. arXiv preprint arXiv:1410.4919
Wang GL, Yang PC (2010) A recent approach incorporating external forces to predict nonstationary processes. Atmospheric and Oceanic Science Letters 03(3):151–154
Wang PF, Huang G, Wang Z (2006) Analysis and application of multiple-precision computation and round-off error for nonlinear dynamical systems. Adv Atmos Sci 23(5):758–766
Wang GL, Yang PC, Bian JC, Zhou XJ (2011) A novel approach in predicting non-stationary time series by combining external forces. Science Bulletin 56(Z2):3053–3056
Wang PF, Li JP, Li Q (2012) Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of Lorenz equations. Numerical Algorithms 59(1):147–159
Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D Nonlinear Phenomena 16(3):285–317
Acknowledgements
This work is supported by the National Natural Sciences Foundation of China (41375112, 41530426, and 41575058) and the CAS Key Technology Talent Program.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, P., Pan, X. The reliable solution and computation time of variable parameters logistic model. Theor Appl Climatol 132, 851–855 (2018). https://doi.org/10.1007/s00704-017-2136-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00704-017-2136-3