On some necessary and sufficient conditions for a recurrent neural network model with time delays to generate oscillations

Authors:
Chunhua Feng;Réjean Plamondon;Christian O'Reilly
Affiliations:
College of Mathematical Sciences, Guangxi Normal University, Guilin, China;Laboratoire Scribens, Département de Génie Électrique, École Polytechnique de Montréal, Montréal, QC, Canada;Laboratoire Scribens, Département de Génie Électrique, École Polytechnique de Montréal, Montréal, QC, Canada
Venue:
IEEE Transactions on Neural Networks
Year:
2010

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Abstract

In this paper, the existence of oscillations for a class of recurrent neural networks with time delays between neural interconnections is investigated. By using the fixed point theory and Liapunov functional, we prove that a recurrent neural network might have a unique equilibrium point which is unstable. This particular type of instability, combined with the boundedness of the solutions of the system, will force the network to generate a permanent oscillation. Some necessary and sufficient conditions for these oscillations are obtained. Simple and practical criteria for fixing the range of parameters in this network are also derived. Typical simulation examples are presented.