Self-excited oscillations of a third-order system

A third-order self-excited oscillatory system in the neighbourhood of a stable local integral manifold is investigated. A periodic manifold and a corresponding system in amplitude-phase variables are constructed with approximately the required accuracy. Using the procedure of separation of variables (averaging) the conditions for the existence, uniqueness and stability of self-excited oscillation modes are established, and critical cases of the degeneracy of these conditions are considered. A thermomechanical model of the self-excitation of oscillations inherent in gas-dynamic systems with a heat source is taken as an example. The bifurcation pattern of self-excited oscillations in the space of the governing parameters of the system is investigated in the second approximation.