Theoretical-numerical analysis of wave instabilities is conducted with parametric response function. Fluctuating instantaneous burning rate functionally coupled with pressure fluctuations with phase lag is assumed to examine the validity of the method. With sufficiently large amplitude and less phase lag to perturbation, combustion response is resonant to pressure waves, unstable waves are amplified, and the system is driven to instability. Magnitude of response is a crucial instability parameter in the determination of a stability boundary. make a critical change of balancing conditions between the amplifying and damping acoustic energies. In the in-phase regime, the unstable waves are amplified, whereas, the acoustic waves are attenuated in the out-of-phase regime. In the intermediate regime, no distinct tendency of unstable waves was determined.