Coexistence of multiple continuous attractors for lower-ordered neural networks

Abstract

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.

Keywords:

• Multiple
• continuous attractors
• coexistence
• linear threshold neural network

2010 Mathematics Subject Classifications:

• 34D45
• 34D20
• Attractors
• Stability

Acknowledgements

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

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jiali Yu http://orcid.org/0000-0002-5895-0805

Chunxiao Wang http://orcid.org/0000-0002-8387-5923

Additional information

Funding

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