Inertial manifolds and limit cycles of dynamical systems in ${\mathbb R}^{n}$

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 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.

Keywords

• ordinary differential equations
• limit cycle
• inertial manifold