Nontrivial Global Attractors in 2-D Multistable Attractor Neural Networks

Abstract—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 mathe-matics, 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. Index Terms—Attractor networks, degenerate equilibrium, global attractivity, linear threshold activation function, multistability. I