Coexistence of Multiple Continuous Attractors for Lower-Ordered Neural Networks

A continuous attractor of recurrent neural network is a connected set of stable equilibrium points. It's widely used to interpret a lot of brain activities. A large number of literatures have studied discrete attractors and single continuous attractor. In this paper, the coexisting continuous attractors for nonlinear neural networks is studied and the coexisting conditions of two continuous attractors for network with and without external input in two-dimensional space are obtained by analysing the eigenvalues of the matrix. Finally, all the results are verified by simulation.