Chaotic and pattern recognition properties of a network of Logistic neurons

The literature on chaos theory reports numerous Neural Networks (NNs) in which the individual neurons have been interconnected and designed so that the overall network yields chaotic behaviour. Although such Chaotic Neuron Networks(CNNs) have been extensively studied, the results concerning CNNs which can demonstrate chaos, Associative Memory (AM), and Pattern Recognition (PR) are scanty. Recently, the Adachi NN and its variants have been shown to yield the entire spectrum of these properties as its/their parameters change. In this vein, we investigate the properties of a specific network 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. Indeed, by varying the parameters of the LNN, we show that it can yield AM and PR properties for different settings of the parameters. As far as we know, the results presented here novel, and represent the first NN (other than the Adachi NN) which simultaneously exhibits both chaotic, AM and PR properties.