A hypercycle is a dynamical system formed by different replicator macromolecules that catalyze the reproduction between them in a cyclic architecture. This type of structure is thought to be involved in the transition from simple systems to more complex ones, such as the ones that took place at the origin of life. We conduct a bifurcation study of 5-component asymmetric oscillating hypercycles, in order to see whether there exists a gap between the saddle-node bifurcation value of periodic orbits and the saddle-node bifurcation value of fixed points. To achieve this goal, we carry out both an analytical and a numerical study of the systems and find out that, indeed, there exists a gap, and this one gets larger when the asymmetry of the hypercycle grows
