Statistical Properties of Chaos Associative Memory

In this paper we shall investigate the statistical property and the memory capacity of the chaotic autoassociation memory. The present artificial neuron model is properly characterized in terms of a timedependent sinusoidal activation function to involve a transient chaotic dynamics as well as the energy steepest descent strategy. It is elucidated that the present neural network has a remarkable retrieval ability beyond the conventional models with such a monotonous activation function as sigmoidal one. This advantage is found to result from the property of the analogue periodic mapping accompanied with a chaotic behaviour of the neurons as well as the symmetry of the dynamic equation which may be shown in the invariant measure determined by the Frobenius-Perron equation.

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