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

ABSTRACT

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.

KEYWORDS:

• Line attractors
• continuous attractors
• coupled ring networks
• asymmetric connection weights
• block circulant matrix

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 68T15
• 68T05
• 92B20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant numbers 61572112, 61103041, 61432012, U1435213, 11271001,61370147,61803228], the Applied Basic Research Programs of Science and Technology Department in Sichuan Province [grant number 2019YJ0185].