Simulation and prediction of the process based on the general logistic mapping
Authors: V. V. Skalozub, V. E. Belozеrov, I. V. Klimenko, B. B. Belyy
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Purpose. The aim of the research is to build a model of the generalzed logistic mapping and assessment of the possibilities of its use for the formation of the mathematical description, as well as operational forecasts of parameters of complex dynamic processes described by the time series. Methodology. The research results are obtained on the basis of mathematical modeling and simulation of nonlinear systems using the tools of chaotic dynamics. Findings. A model of the generalized logistic mapping, which is used to interpret the characteristics of dynamic processes was proposed. We consider some examples of representations of processes based on enhanced logistic mapping varying the values of model parameters. The procedures of modeling and interpretation of the data on the investigated processes, represented by the time series, as well as the operational forecasting of parameters using the generalized model of logistic mapping were proposed. Originality. The paper proposes an improved mathematical model, generalized logistic mapping, designed for the study of nonlinear discrete dynamic processes. Practical value. The carried out research using the generalized logistic mapping of railway transport processes, in particular, according to assessment of the parameters of traffic volumes, indicate the great potential of its application in practice for solving problems of analysis, modeling and forecasting complex nonlinear discrete dynamical processes. The proposed model can be used, taking into account the conditions of uncertainty, irregularity, the manifestations of the chaotic nature of the technical, economic and other processes, including the railway ones.