Nontrivial global attractors in 2-D multistable attractor neural networks

Attractor dynamics is a crucial problem for attractor neural networks, as it is the underling computational mechanism for memory storage and retrieval in neural systems. This brief studies a class of attractor network consisting of linearized threshold neurons, and analyzes global attractors based on a parameterized 2-D model. On the basis of previous results on nondegenerate and degenerate equilibria in mathematics, we further elucidate all possible nontrivial global attractors. Our theoretical result provides precise descriptions on how the changes of network parameters affect the attractors' distribution and landscape, and it may give a feasible solution towards specifying attractors by specifying weights. Simulations are presented to illustrate the theoretical results.