Continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons

Authors:
Jiali Yu;Zhang Yi;Jiliu Zhou
Affiliations:
Institute for Infocomm Research, Agency for Science Technology and Research, Singapore;College of Computer Science, Sichuan University, Chengdu, China;College of Computer Science, Sichuan University, Chengdu, China
Venue:
IEEE Transactions on Neural Networks
Year:
2010

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Abstract

Continuous attractors of Lotka-Volterra recurrent neural networks (LV RNNs) with infinite neurons are studied in this brief. A continuous attractor is a collection of connected equilibria, and it has been recognized as a suitable model for describing the encoding of continuous stimuli in neural networks. The existence of the continuous attractors depends on many factors such as the connectivity and the external inputs of the network. A continuous attractor can be stable or unstable. It is shown in this brief that a LV RNN can possess multiple continuous attractors if the synaptic connections and the external inputs are Gussian-like in shape. Moreover, both stable and unstable continuous attractors can coexist in a network. Explicit expressions of the continuous attractors are calculated. Simulations are employed to illustrate the theory.