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.
2010 Mathematics Subject Classifications:
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