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Working paper

Inertial Manifolds and Limit Cycles of Dynamical Systems in Rn

arxiv.org. math. Cornell University, 2019. No. 1911.03932.
A.V. Romanov, Kondratieva L.
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 Poincare–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.