Continuous attractors and population decoding multiple-peaked activity

A continuous attractor of network is a set of connected stable equilibrium points and it has been recognized as a suitable model for describing the encoding of continuous stimuli in neural networks. Population coding is a method to represent stimuli by using the collective activities of a number of neurons. It is difficult to extract information from these population codes because of the noise inherent in neuronal responses. In this paper the dynamics analysis of a population decoding model is investigated. The conditions of the population decoding model to possess nonzero continuous attractor are derived. Moreover the explicit expressions of the continuous attractors are provided. Simulations are employed to illustrate the theory.