Stability Gap between Off- and On-Firing States in a Coupled Ginzburg-Landau Oscillator Neural Network

An oscillator neural network based on the Ginzburg-Landau equation is proposed in order to investigate associative memory. The embedded patterns include both offand on-firing states with phase. Neurons encode not only the phase but also the state of the cell. The system has a Lyapunov function with wells corresponding to offand on-firing states. These two states are characterized by mutual stabilities which are generally different. Each neuron falls into one of the wells, as determined by its dynamics. The storage capacity and the order parameter overlap are studied using numerical simulations and an ordinary self-consistent signal-to-noise analysis. We show that these properties depend crucially on both the potential parameter and the mean activity levels of the patterns. In the case of the sparse coding limit, the storage capacity diverges as in the case of the binary model.