Analysis of periodic perturbations of limit cycles

An algorithm due to Loud is used to find asymptotically convergent series solutions for limit cycles subjected to weak periodic perturbations. If an exact or approximate solution to the unperturbed limit cycle is available near or far from marginal stability, then accurate predictions can be made for entrainment bands and the phase relationships between the various oscillatory chemical species and the perturbation. The utility of this method is shown for several model systems. In an appendix, the appearance and character of critical slowing down at the edges of entrainment bands is demonstrated.