The Koper model is a vector field that was developed to study electrochemical oscillations arising in diffusion processes. In the framework of this paper, we consider the Koper model of chemical reactors. It is a three-dimensional autonomous slow-fast system with a folded node and a supercritical singular Hopf bifurcation. The aim is to construct the expansion of invariant manifold with variable stability and corresponding gluing function using the flow curvature method. We show that Koper model has sufficiently smooth invariant surface, called black swan. Computer simulation and computer algebra methods are used for the quantitative analysis of the model.

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Modeling of critical phenomena is a very important problem, which has direct applied application in many branches of science and technology. In this paper we regard a modification of the low curvature method applied to construction of invariant manifolds of autonomous fast-slow dynamic systems. We compared a new method with original ones via finding duck-trajectories and their multidimensional analogues surfaces with variable stability. Comparison was used a three-dimensional autocatalytic reaction model and a model of the burning problem.

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