Vas Gabriella
(Szegedi Tudományegyetem, Bolyai Intézet,
MTA-SZTE Analízis és Sztochasztika Kutatócsoport)
The unstable set of a periodic orbit for delayed positive feedback
Absztrakt:
In
the paper [Krisztin, T., Vas, G., Large-amplitude periodic solutions
for differential equations with delayed monotone positive feedback,
JDDE 23, no. 4, 727–790], we have constructed large-amplitude periodic
orbits for an equation with delayed monotone positive feedback. We have
shown that
the unstable sets of the large-amplitude periodic orbits constitute the
global attractor besides spindle-like structures.
The
purpose of this talk is to characterize the geometric structure of one
of these unstable sets. We show that it is a C^{1}-submanifold of the
phase space, determine its dimension, and give a so-called global graph
representation.
This research was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP-4.2.4.A/ 2-11/1-2012-0001 ‘National Excellence Program’.
