Line attractors of coupled ring neural networks with block circulant weight matrix

摘要

The continuous attractors of neural networks with symmetric connection weights have been studied widely. However, most of the matrices are asymmetric. In this paper, the model is coupled by some subnetworks. The connection weight matrix of each subnetwork is a circulant matrix, so the whole connection matrix is a block circulant matrix which is asymmetric. The conditions that guarantee this model with block circulant connection weight matrix to possess continuous attractor is obtained. Furthermore, the continuous attractor is a one-dimensional line attractor.