Sequential retrieval of non-random patterns in a neural network

A neural network capable of retrieval of sequential patterns is analysed. The authors treat the network proposed by Buhmann and Schulten (1987). Although they concluded that the thermal noise induces retrieval of sequential patterns, the authors show that the network has limit cycle solutions even at zero temperature. Behaviour of the network at high temperatures is also analysed. The transition temperatures between a high-temperature fixed point phase and a limit cycle phase are calculated numerically to draw a phase diagram. The characteristic features of the phase diagram are discussed. The reentrant transition temperatures between the limit cycle and low-temperature fixed point phases are calculated analytically.