Two forms of stability change for integral manifolds (Q2387947)

The paper is devoted to the study of different types of stability change of the slow manifold for singularly perturbed systems. Namely, the case when the corresponding linearized matrix has a real eigenvalue passing through zero, and the case when the matrix has two complex conjugate eigenvalues crossing the imaginary axis. In the last case, the phenomenon of delayed loss of stability can be observed. The author describes conditions for the existence of duck trajectories and shows that in that case when the system has an additional control function there exists an attracting-repulsive manifold consisting of duck trajectories. The same result can be obtained for the case of delayed loss of stability.