Effect of constant external input on continuous attractors shifting

The dynamics of a class of recurrent neural networks with uniform constant external input is investigated in this paper. Nowadays, continuous attractors have been recognized as promising model for describing the encoding of continuous stimuli in neural networks. The existence of the continuous attractors depends on a lot of factors such as connection weight and the external input and so on. The external input is very important in allowing the network to exhibit such an interesting character. Small changes in this external input level may shift a network from a relatively quiet state to some other state with highly complex dynamics. Thus, the external input may act as a switch that allows networks to be turned on or off regardless of their function. In this paper we find when the external input changes from zero to a small positive value, the steady state of network will shift from one continuous attractor to another. It shows how the external input controls the state of networks. Examples and simulation results are used to illustrate the theory.