Complex dynamics in discrete delayed models with D4D4 symmetry

In this paper, we consider nonlinear time-delayed models with four identical resonators. Detailed analysis about equivariant bifurcations coupled with the Lie group actions on vector spaces is offered, including equivariant Neimark–Sacker bifurcations, equivariant pitchfork bifurcations and equivariant periodic doubling bifurcations. Pattern formation, spatio-temporal behavior and mode interactions are shown in a discrete nonlinear optical model involving a time-delayed feedback.