A parametric study of the CVRC combustor test case is carried out by a quasi-1D Eulerian solver including a pressure lag response function which is used to take into account the unsteady heat release, typically driving combustion instability phenomena. The parameters under investigation are those defining the selected response function that are its amplitude and characteristic time lag. Both stable and unstable cases have been obtained for a wide range of amplitude and time lag which allow to investigate limit cycles at moderate amplitude. The extension of the approach to even higher amplitude of limit cycles of the order of those actually obtained in CVRC is presently in progres