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arXiv · 1911.03932

Inertial Manifolds and Limit Cycles of Dynamical Systems in $\mathbb R^n$

L. A. Kondratieva·A. V. Romanov
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Abstract

We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in ${\mathbb R}^{n}$ 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.

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L. A. Kondratieva, A. V. Romanov. 2019-11-10. Inertial Manifolds and Limit Cycles of Dynamical Systems in $\mathbb R^n$. https://arxiv.org/abs/1911.03932

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