abstract.txt

Although the established theory of non-linear dynamical systems is effective at
describing physical systems and phenomena, the theory has been developed with a
focus on smooth systems, limiting its applicability in certain areas. This
limitation becomes apparent when modeling piecewise-smooth systems such as
electrical systems that contain at least one switching element or mechanical
systems with collisions. This thesis deals with a model of a DC/AC power
converter that is piecewise-smooth, discontinuous, and has a certain symmetry.
The definition of this model is exceptionally complex, and the model exhibits
an unusual period-incrementing structure that is affected by multistability.
This thesis identifies the characteristics of the model that lead to this
unusual bifurcation structure by constructing an archetypal model that exhibits
the same bifurcation behavior. It follows a description of the dynamics of the
archetypal model and an explanation of the bifurcation structure using the
description of the dynamics. Additionally, this thesis demonstrates that the
proposed archetypal model can exhibit behavior leading to bifurcation
structures that are related to period-adding structures. The resulting
bifurcation structures behave unexpectedly, and this behavior is explained by
leveraging the symmetry present in both the archetypal and the original model.
Using the symmetry present, the mathematical rules governing the resulting
bifurcation structures are derived from the rules governing classical
period-adding structures.