Development of neural models for the logistic equation and study of the neural based trajectories in the convergence, periodic, and chaotic regions

Authors:
Athanasios Margaris;Manos Roumeliotis;Miltiadis Adamopoulos
Affiliations:
Department of Applied Informatics, University of Macedonia;Department of Applied Informatics, University of Macedonia;Technological Educational Institute of Thessaloniki, Department of Informatics
Venue:
Neural, Parallel & Scientific Computations
Year:
2001

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Abstract

This paper examines the ability of neural based structures to model the logistic equation. This modeling includes not only the generation of the logistic curve, but also the time series that are generated by the logistic neural model. This study is applied to the three main regions of the logistic equation: the region of convergence for parameter values less than 3, the periodic region for parameter values in the interval [3, 3.57], and the chaotic region for values in the interval [3.57, 4]. For each region the fixed points of the logistic map are calculated and compared to the corresponding theoretical points. In addition, the distribution of the absolute mean error between the theoretical and the experimental curves is also studied. Finally, the Lyapunov exponent for both the theoretical and the neural based time series is estimated.