named after Academician S.P. Korolyov In the framework of this paper we consider the fl ow curvature method applying to modeling critical phenomena in one of the three-timescale fast-slow autonomous dynamical systems. The article considers a model that is a generalization of the classical Van der Pol model. The approximations of an invariant manifold and a two-dimensional analogue of a duck trajectory (a black swan) are constructed.