An oscillatory criterion for a time delayed neural ring network model

The effects of delays on dynamical networks and the stability analysis of time delayed systems have received a notable attention over the past decades. In this paper, the effects of delays on the oscillatory properties of a neural ring networks model are considered. The existence of oscillations for a specific type of recurrent neural network with time delays between neural interconnections is investigated. By using Chafee's closed orbit theory, some sufficient conditions for permanent oscillations are obtained. Simple and practical criteria for selecting the range of parameters in this network model are also derived. Among other things, the solutions that we provide can be applied to various activation functions. A few computer simulations are presented to support our analysis. The present study can be applied to analyze under which conditions a ring network could be exploited as an oscillatory pattern generator.

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