Flow version of statistical neurodynamics for oscillator neural networks

We consider a neural network of Stuart–Landau oscillators as an associative memory. This oscillator network with N elements is a system of an N-dimensional differential equation, works as an attractor neural network, and is expected to have no Lyapunov functions. Therefore, the technique of equilibrium statistical physics is not applicable to the study of this system in the thermodynamic limit. However, the simplicity of this system allows us to extend statistical neurodynamics [S. Amari, K. Maginu, Neural Netw. 1 (1988) 63–73], which was originally developed to analyse the discrete time evolution of the Hopfield model, into the version for continuous time evolution. We have developed and attempted to apply this method in the analysis of the phase transition of our model network.