Continuous Attractor that Appears in Autoassociative Memory Model Extended to XY Spin System

We analyzed the attractor structure in an autoassociative memory model extended to an XY spin system. We examined the attractor structures for two kinds of memory patterns: one composed of two states, 0 and pi; and the other composed of an infinite number of states [0, 2 pi). To focus on analyzing the attractor structure, we used a finite number of memory patterns. As a result of our study, we found that memory patterns composed of two states are acquired not as point attractors but as a continuous (line) attractor, and that the retrieval state of the model can change without the free energy changing from one memory pattern to another. The memory patterns are acquired as point attractors in an autoassociative memory model of an Ising spin system. Therefore, the attractor structure is changed markedly by extending the autoassociative memory model to an XY spin system. Furthermore, we found that the attractor structure changes depending on the number of states in the memory pattern, and that the memory patterns composed of an infinite number of states are not acquired as a continuous attractor.