Weakly Connected Oscillatory Network Models for Associative and Dynamic Memories

Several studies in neuroscience have shown that nonlinear oscillatory networks represent bio-inspired models for information and image processing. Recent studies on the thalamo-cortical system have shown that weakly connected oscillatory networks (WCONs) exhibit associative properties and can be exploited for dynamic pattern recognition. In this manuscript we focus on WCONs, composed of oscillators that adhere to 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 variation of each oscillator, due to weak coupling). Firstly a very accurate analytic expression of the phase deviation equation is derived, by jointly describing the function technique and the 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 WCONs are presented as examples of associative and dynamic memories.