Three cell symmetry discrete-time-delayed neural network

In this paper, we consider several three-dimension discrete neural network models representing the models containing symmetry with time-delayed connections. The existence of symmetric property is investigated. We examine the relation between the structure of a discrete network and the spatio-temporally symmetric periodic dynamics it can support. We illustrate the existence of spatio-temporally periodic solutions through a direct construction of symmetric groups, and show that these solutions can be stable in some region of parameter space. We give computer simulations to support the theoretical predictions.