Two-dimensional Continuous Attractors of Recurrent Neural Networks

In order to facilitate periodic membrane oscillations in brain, continuous attractors with periodic shape has been studied in the CANN. This paper will extend one-dimensional continuous attractors with periodic shape to two-dimensional ones in Recurrent Neural Networks (RNN). Under a certain condition, the RNN can possess the stable and unstable two-dimensional (2D) continuous attractors. Finally, a example is used to illustrate the 2D periodic continuous attractors.