Pattern formation in a symmetrical network with delay

In this paper, we investigate the codimension one bifurcation involved in a symmetrical ring network with eight coupled cells. Combining the related theoretical foundations, including the symmetric bifurcation theory, representation theory of Lie groups, center manifold theorem and normal form method for functional differential equations, we address the pattern formation induced from the primary codimension one bifurcation. Numerical simulations are given to illustrate the theoretical predictions.