Stability of oscillatory retrieval solutions in the oscillator neural network without Lyapunov functions

Constructing a Ginzburg-Landau map neural network, we analyze its storage capacity with an equilibrium theory of the self-consistent signal-to-noise analysis (SCSNA); however, the prediction does not consist with the simulation results just in the parameter region where the characteristic of the non-Lyapunov-function system gets enhanced [J. Phys. A 32, 4623 (1999)]. It is expected that this inconsistency comes from the fact that the dynamics of retrieval and nonretrieval states governs the phase transition. Alternatively, we investigate its storage capacity with the help of the Amari-Maginu-Okada theory, a dynamical theory, for the stability analysis of dynamical states. We consequently found that the theory predicts dynamical states quite well especially in the region where the SCSNA breaks down, and that the phase diagram coincides quantitatively well with the simulation results.