Networking logistic neurons can yield chaotic and pattern recognition properties

Abstract

Over the last few years, the field of Chaotic Neural Networks (CNNs) has been extensively studied because of their potential applications in the understanding/recognition of patterns and images, their associative memory properties, their relationship to complex dynamic system control, and their capabilities in the modeling and analysis of other measurement systems. However, the results concerning CNNs which can demonstrate chaos, quasi-chaos, Associative Memory (AM), and Pattern Recognition (PR) are scanty. In this paper, we consider the consequences of networking a set of Logistic Neurons (LNs). By appropriately defining the input/output characteristics of a fully connected network of LNs, and by defining their set of weights and output functions, we have succeeded in designing a Logistic Neural Network (LNN) possessing some of these properties. The chaotic properties of a single-neuron have been formally proven, and those of the entire network have also been alluded to. Indeed, by appropriately setting the parameters of the LNN, we show that the LNN can yield AM, chaotic and PR properties for different settings. As far as we know, the results presented here are novel, and the chaotic PR properties of such a network are unreported.