Nonlinear Phenomena in Complex Systems, 2003, Vol.6, No.4, pp.861-869

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2003, Vol.6, No.4, pp.861-869

Sufficient Conditions for Retrieval of Memorized Patterns by Analog Neural Networks with Synaptic and Input Wiener Noise
A.V. Kartynnick and A.D. Linkevich

A stochastic generalization of the Hopfield analog neural networks was analytically investigated. The phase space of the Hopfield analog neural network was studied in the case when synaptic coupling constants were adjusted with the aid of the projection learning algorithm which exploits outer products of vectors. The shape and size of basins of attractors around the memorized patterns are found to be drastically dependent on the network and the learning rule parameters.
Key words: information processing, associative memory, retrieval of memorized patterns, neural network, Wiener synaptic noise, Wiener input (threshold) noise, Ito stochastic differential equations, Lyapunov function

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