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Kondratieva L., A.V. Romanov. Electronic Journal of Qualitative Theory of Differential Equations. 2019. No. 96. P. 1-11.

We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in Rn permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincaré–Bendixson theory. In the case n = 3 we implement such a scenario for a model of a satellite rotation around a celestial body of small mass and for a biochemical model.

Added: Dec 22, 2019