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An algorithm due to Loud is used to fmd 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.

The kinetics of the hydration of 2,3-epoxy-1-propanol to glycerine in a continuous stirred tank reactor is studied both numerically and analytically. The agreement between our numerical and analytical results, and others' experimental measurements is extremely good for the autonomous system; we predict and then verify numerically the existence of normal and inverted Hopf bifurcations. We then periodically perturb the system to obtain details of entrainment: Entrainment bandwidths, phase locking, and resonance in the amplitudes of temperature and concentrations. We also numerically calculate the dissipation and find at fixed chemical flux, conversion rate, and average output temperature, that the total dissipation is unchanged under resonance conditions, but the dissipated energy can be varied among the different heat baths and free energy sinks by varying the perturbation frequency.

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