Center manifold of the viscous Moore-Greitzer PDE model

A commonly used mathematical model for jet engines that captures the ow beh avior of a compression system, known as the viscous Moore-Greitzer PDE mode l, consists of a PDE and two ODEs. The PDE describes the behavior of distur bances in the inlet region of the compression system, and the two ODEs desc ribe the coupling of the disturbances with the mean ow. In this paper, we s tudy this full-order model and rst show that it is not topologically equiva lent to its linearized version near the point where the pressure rise reach es its maximum. We further show that the model features a center manifold n ear this maximum pressure rise, which makes it possible to translate the st udy of the behavior of the local ow in the compressor into a study of the f low of two scalar differential equations on the center manifold, which we c arry out explicitly in the paper.