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Studies have been carried out on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule such as the Hopfield model. The relative phase informations, the in phase and antiphase, can be embedded in the network. By self-consistent signal-to-noise analysis, it was found that the storage capacity is given by ␣ c ϭ0.042, which is better than that of Cook's model. However, the retrieval quality is worse. In addition, an investigation was made into an acceleration effect caused by asymmetry of the phase dynamics. Finally, it was numerically shown that the storage capacity can be improved by modifying the shape of the coupling function.

Analytic treatment of a non-equilibrium random system with large degrees of freedoms is one of most important problems of physics. However, little research has been done on this problem as far as we know. In this paper, we propose a new mean field theory that can treat a general class of a nonequilibrium random system. We apply the present theory to an analysis for an associative memory with oscillatory elements, which is a well-known typical random system with large degrees of freedoms.