On one scenario for changing the stability of invariant manifolds of singularly perturbed systems

The article is devoted to the peculiarities of stability change of slow invariant manifolds of singularly perturbed systems of ordinary differential equations. It should be noted that the change of stability of invariant manifolds can proceed according to different scenarios. In addition to two well-known scenarios of this phenomenon, one more scenario is considered in this paper. To demonstrate the peculiarities of the stability change of slow invariant manifolds under this scenario, a number of examples are proposed. The existence theorem of an exact invariant manifold with stability change for some class of singularly perturbed systems of ordinary differential equations is obtained.