Local bifurcations in differential equations with state-dependent delay
Sieber, J
Date: 1 November 2017
Journal
Chaos
Publisher
AIP Publishing
Publisher DOI
Abstract
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations
of equilibria. As most of these normal forms have been classified and analysed, finding which particular class
of normal form one encounters in a numerical bifurcation study guides follow-up computations.
This paper builds on ...
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations
of equilibria. As most of these normal forms have been classified and analysed, finding which particular class
of normal form one encounters in a numerical bifurcation study guides follow-up computations.
This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay
that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods
to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of
local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which
phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all
invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also
in the full sd-DDE
Mathematics and Statistics
Faculty of Environment, Science and Economy
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