Reanalysis of a Castor model limit cycle calculation

The Castor equation is a third-order, nonlinear, ordinary differential equation that was derived to model pulsations for stars having oscillatory changes in their radii as reflected through their light output. A detailed study of this model was done by J.P. Cox, based on unpublished notes of J. Castor. The purpose of the current work is to re-examine these calculations and indicate that results different from those of Castor and Cox are obtained by use of a different method. An explanation for this is given.