A GCM Neural Network with Piecewise Logistic Chaotic Map

Abstract

In order to explore dynamic mechanisms and chaos control of globally coupled map (GCM) chaotic neural networks, a new GCM model, called the PL-GCM model is proposed, of which a piecewise logistic chaotic map is used instead of a logistic map. As a result of the strong chaotic features of the map, the neurons’ period and chaotic characteristics over a wide range of parameters are discussed, the dynamic mechanism is demonstrated in detail, and the numerical simulations such as state evolution, the largest Lyapunov exponent (LLE), contour map, and so on are exhibited. Furthermore, chaos control of the proposed PL-GCM model is investigated by adopting two chaos control methods. It is shown that the network with conventional coupling or delay coupling can be precisely controlled to any specified periodic orbit by feedback control, and its dynamic associative memory is realized by the variable threshold parameter control method with external information. The results of simulations and experiments suggest that the network is controlled successfully and can output period patterns with a specified period that contains the stored pattern closest to the initial pattern. All features suggest that the network is fit for pattern recognition and information processing.