Dynamical properties of background neural networks with uniform firing rate and background input

In this paper, the dynamic properties of the background neural networks with the uniform firing rate and background input is investigated with a series of mathematical arguments including nondivergence, global attractivity and complete stability analysis. Moreover, it shows that shifting the background level affects the existence and stability of the equilibrium point. Depending on the increase or decrease in background input, the network can engender bifurcation and chaos. It may be have one or two different stable firing levels. That means the background neural network can exhibit not only monostability but also multistability.