Dynamical phase diagrams of neural networks with asymmetric couplings
M. N. Tamashiro, Osame Kinouchi, Silvio R. A. Salinas · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997
We consider the synchronous updating of a fully connected Ising neural network with separable but asymmetric couplings. In the thermodynamic limit, and away from saturation, it is possible to write a nonlinear mapping for the time evolution of the macroscopic order parameters. A detailed analysis of this mapping is performed for a simple case, with p=2 stored patterns. The dynamical phase diagram, in terms of the degree of noise and the parameters of the embedding matrix, displays a rich structure of locked regions into different cycles, in association with nonstandard Farey trees. In some regions of the dynamical phase diagram, we show the coexistence of two different Farey sequences, giving rise to the overlapping of several locked regions.