Online at stacks.iop.org/Non/21/1547

We show that generic Hopf–Neı̆mark–Sacker bifurcations occur in the dynamics of a large class of feed-forward coupled cell networks. To this end we present a framework for studying such bifurcations in parametrized families of perturbed forced oscillators near weak resonance points. Our approach is based on fine-tuning existing normal form techniques. We then apply this framework to show that certain cells in the feed-forward networks exhibit this forced oscillator dynamics and, hence, undergo generic Hopf–Neı̆mark–Sacker bifurcations. These bifurcations correspond to the occurrence of resonance tongues in parameter space with a ‘standard ’ geometry. Mathematics Subject Classification: 37G15, 34C25, 34C27 (Some figures in this article are in colour only in the electronic version) 1