Oscillatory associative memory network with perfect retrieval

Inspired by the discovery of possible roles of synchronization of oscillations in the brain, networks of coupled phase oscillators have been proposed before as models of associative memory based on the concept of temporal coding of information. Here we show, however, that error-free retrieval states of such networks turn out to be typically unstable regardless of the network size, in contrast to the classical Hopfield model. We propose a remedy for this undesirable property, and provide a systematic study of the improved model. In particular, we show that the error-free capacity of the network is at least 2ε² / log n patterns per neuron, where n is the number of oscillators (neurons) and ε the strength of the second-order mode in the coupling function.