Dynamics Of Chaotic Neural Network Research Articles

Dynamic depression control of chaotic neural networks for associative memory

The chaotic neural network constructed with chaotic neurons presents complex dynamics and has potential application in the associative dynamics and information processing. However, the states of the chaotic neural network wander around all the stored patterns and cannot be stabilized to one of the stored patterns or a periodic orbit because of the chaotic characteristic of the network, which hampering the application of the chaotic associative dynamics of chaotic neural network to information processing. In this work, a dynamic depression control method imposed on the internal state of neurons for chaotic neural networks is proposed. In this way, the decay parameters and the scaling parameter for the refractoriness are time varying determined by the internal state of neurons. Ascribing to dynamic depression control, chaos is controlled in a self-adaptive manner and no target needs to be specified in advance. Furthermore, the theoretic analysis of dynamic depression control is presented. The numerical simulation proves that the chaos in the chaotic neural network can be controlled with the dynamic depression control, and the neural network can be stabilized to a stored pattern if the control strength parameter is chosen suitable.

Associative memory with a controlled chaotic neural network

A chaotic neural network (CNN) composed of chaotic neurons exhibits chaotic associative dynamics for some values of the parameters, which indicate that the CNN is a promising technique that can be applied to information processing such as pattern recognition and memory recalling. However, the outputs of the CNN in those parameter areas wander around all the stored patterns and cannot be stabilized to one of the stored patterns or a periodic orbit because of its chaotic behavior. Furthermore, it is also difficult to judge when the chaotic dynamics must be terminated, thereby hampering the application of the chaotic associative dynamics of CNNs to information processing. In this paper, we propose a novel chaos control scheme, i.e. a parameter modulated control method, for the CNN, which is applied particularly for associate memory. This scheme can be viewed as a type of adaptive control method in which the refractory scaling parameter decreases by the addition of a delay feedback control signal to the network. By means of this control method, the outputs of the controlled CNN converge to the periodic orbits and are dependent on the initial patterns. We observed that the controlled CNN can distinguish two initial patterns even if they have a small difference. This implies that such a controlled CNN can be feasibly applied to information processing such as pattern recognition.

Effects of correlation among stored patterns on associative dynamics of chaotic neural network

We numerically investigate the effects of correlation among stored patterns on the associative dynamics in a chaotic neural network model. In the model, there are two kinds of parameters: one is a measure of the Hopfield like behavior of the retrieval process and another controls the chaotic behavior. The parameter dependence of the associative dynamics is also examined. The following results are found. (i) Two dimensional parameter space is divided into two kinds of associative states by a distinct boundary. One is the retrieval state of the association such as the Hopfield like retrieval state, and another is the wandering state of the associative dynamics where the network retrieves stored patterns and their reverse patterns. (ii) The area of the wandering state becomes larger as the degree of correlation becomes larger. (iii) As the degree of correlation becomes larger, both the recall ratio of correlated patterns and the transition frequency between correlated patterns becomes larger in the wandering state. (iv) The whole region of the wandering state in the parameter space is not necessarily chaotic from the view point of the Lyapunov dimension, but most of the region of the wandering state is chaotic.