Yu Jiali, Yi Zhang, Zhou Jiliu
Institute for Infocomm Research, Agency for Science Technology and Research, 138632, Singapore.
IEEE Trans Neural Netw. 2010 Oct;21(10):1690-5. doi: 10.1109/TNN.2010.2067224. Epub 2010 Sep 2.
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.
本文简要研究了具有无限神经元的Lotka-Volterra递归神经网络（LV RNN）的连续吸引子。连续吸引子是相连平衡点的集合，并且已被认为是用于描述神经网络中连续刺激编码的合适模型。连续吸引子的存在取决于许多因素，例如网络的连通性和外部输入。连续吸引子可以是稳定的或不稳定的。本文表明，如果突触连接和外部输入呈高斯形状，则LV RNN可以拥有多个连续吸引子。此外，稳定和不稳定的连续吸引子可以在一个网络中共存。计算了连续吸引子的显式表达式。通过仿真来说明该理论。
