Weakly Connected Oscillatory Networks as Associative and Dynamic Memories

Many studies in neuroscience have shown that nonlinear oscillatory networks represent a bio-inspired models for information and image processing. Studies on the thalamo-cortical system have shown that weakly connected oscillatory networks (WCNs) exhibit associative properties and can be exploited for dynamic pattern recognition. In this manuscript we focus on WCNs, composed of oscillators that admit of a Lur'e like description and are organized in such a way that they communicate one another, through a common medium. The main dynamic features are investigated by exploiting the phase deviation equation (i.e. the equation that describes the phase deviation due to the weak coupling). Firstly a very accurate analytic expression of the phase deviation equation is derived, via the joint application of the describing function technique and of Malkin's theorem. Furthermore, by using a simple learning algorithm, the phase-deviation equation is designed in such a way that given sets of patterns can be stored and recalled. In particular, two models of WCNs are given as examples of associative and dynamic memories