A Third-Order Differential Equation Modelling Stellar Pulsation*

We investigate the properties of the solutions to a third-order nonlinear ODE modeling the radial oscillations of a star. A summary of previous work on this equation has been presented by Cox [1]. Their calculations are based on the use of a two-time perturbation method to determine the possible existence and stability of limit-cycles. We demonstrate that the application of phase-space techniques and the Hopf bifurcation theorem gives results that differ from those reported by Cox. [1] J. P. Cox, Theory of Stellar Pulsation (Princeton University Press, 980), section 13.4.