Inertial Manifolds and Limit Cycles of Dynamical Systems in \mathbb Rⁿ

2019/11/10 by Liudmila Kondratieva, Kondratieva, L. A., A. V. Romanov +1
Engineering · Physics and Astronomy · #34C07 #34C45 #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1911.03932

openalex publication_date 2019/11/10 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28

Abstract

We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in \mathbb 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.

Related

• The Poincaré-Bendixson theory for certain compact semi-flows in Banach spaces
• Proving the existence of numerically detected planar limit cycles
• Limit Cycle Analysis of 3-D Nonlinear systems
• Transversal conics and the existence of limit cycles
• Partial Inertial Manifolds for infinite-dimensional dynamical systems: Example for P.D.E.s with a state-dependent delay