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Original Articles

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

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Pages 687-699 | Received 24 Oct 2017, Accepted 13 Feb 2019, Published online: 18 Mar 2019
 

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.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

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].

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