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that are equivalent in this situation is satisfied, then equation (1.1) generates a Csmooth phase flow {Φt∈R} in R . Everywhere below we identify linear operators on R with their matrices. Let f = −A + F be a vector field of (1.1), then we call xs ∈ R n a singular point if f(xs) = 0. By a cycle we mean a closed trajectory. A stable limit cycle is a cycle that is asymptotically orbitally stable as t→ +∞.

electronic journal on the qualitative theory of differential equations

Inertial manifolds and limit cycles of dynamical systems in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math>

Inertial manifolds and limit cycles of dynamical systems in R 2