title: Continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons.
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.
authors.affiliation: Institute for Infocomm Research, Agency for Science Technology and Research, 138632, Singapore. jlyu@i2r.a-star.edu.sg
authors.forename: Jiali
authors.initials: J
authors.lastname: Yu
authors.forename: Zhang
authors.initials: Z
authors.lastname: Yi
authors.forename: Jiliu
authors.initials: J
authors.lastname: Zhou
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008433:Mathematics; D009415:Nerve Net / Q000502:physiology; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*