Continuous Attractors of Lotka-Volterra Recurrent Neural Networks

Authors:
Haixian Zhang;Jiali Yu;Zhang Yi
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, P.R. China 610054;School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, P.R. China 610054;Machine Intelligence Laboratory, School of Computer Science, Sichuan University, Chengdu, P.R. China 610065
Venue:
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Year:
2009

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Abstract

Continuous attractor neural network (CANN) models have been studied in conjunction with many diverse brain functions including local cortical processing, working memory, and spatial representation. There is good evidence for continuous stimuli, such as orientation, moving direction, and the spatial location of objects could be encoded as continuous attractors in neural networks. Although their wide applications for the information processing in the brain, representation and stability analysis of continuous attractors in non-linear recurrent neural networks (RNNs) have been reported very little so far. This paper studies the continuous attractors of Lotka-Volterra (LV) recurrent neural networks. Conditions are given to insure the network has continuous attractors. Representation of continuous attractor is obtained under the conditions. Simulations are employed to illustrate the theory.