Continuous attractors of discrete-time recurrent neural networks

This paper studies the continuous attractors of discrete-time recurrent neural networks. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. Continuous attractors of neural networks have been used to store and manipulate continuous stimuli for animals. A continuous attractor is defined as a connected set of stable equilibrium points. It forms a lower dimensional manifold in the original state space. Under some conditions, the complete analytical expressions for the continuous attractors of discrete-time linear recurrent neural networks as well as discrete-time linear-threshold recurrent neural networks are derived. Examples are employed to illustrate the theory.