Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global recurrent multi-layer perceptrons. We show formally that it is possible to make these iterations behave chaotically, as defined by Devaney, and thus we obtain the first neural networks proven chaotic. Several neural networks with different architectures are trained to exhibit a chaotical behavior.
This research investigates the potential utility of chaotic dynamics in neural information processing. A novel chaotic spiking neural network model is presented which is composed of non-linear dynamic state (NDS) neurons. The activity of each NDS neuron is driven by a set of non-linear equations coupled with a threshold based spike output mechanism. If time-delayed self-connections are enabled then the network stabilises to a periodic pattern of activation. Previous publications of this work have demonstrated that the chaotic dynamics which drive the network activity ensure that an extremely large number of such periodic patterns can be generated by this network. This paper presents a major extension to this model which enables the network to recall a pattern of activity from a selection of previously stabilised patterns. The basic premise of this research is that deterministic chaos is a powerful mechanismfor the storage and retrieval of information in the dynamics of artificial neuralnetworks. Substantial evidence has been found in biological studies for the presenceof chaos in the dynamics of natural neuronal systems [1-3]. Many have suggestedthat this chaos plays a central role in memory storage and retrieval [1,4-6]. Indeed,chaos offers many advantages over alternative memory storage mechanisms used inartificial neural networks. One is that chaotic dynamics are significantly easier tocontrol than other linear or non-linear systems, requiring only small appropriatelytimed perturbations to constrain them within specific Unstable Periodic Orbits(UPOs). Another is that chaotic attractors contain an infinite number of these UPOs.If individual UPOs can be made to represent specific internal memory states of asystem, then in theory a chaotic attractor can provide an infinite memorystore for thesystem. In this paper we investigate the possibility that a network can self-selectUPOs in response to specific dynamic input signals. These UPOs correspond tonetwork recognition states for these input signals. Abstract A model of a single neuron with chaotic dynamics is proposed by considering the following properties of biological neurons: (1) graded responses, (2) relative refractoriness and (3) spatio-temporal summation of inputs. The model includes some conventional models of a neuron as its special cases; namely, chaotic dynamics is introduced as a natural extension of the former models. Chaotic solutions of both the single chaotic neuron and the chaotic neural network composed of such neurons are numerically demonstrated.