  The flow of contracting systems contracts 1-dimensional polygons (i.e. lines)
at an exponential rate. One reason for the usefulness of contracting systems is
that many interconnections of contracting sub-systems yield an overall
contracting system. A recent generalization of contracting systems is called
$k$-contracting systems, where $k\in\{1,\dots,n\}$. The flow of such systems
contracts $k$-dimensional polygons at an exponential rate, and in particular
they reduce to contracting systems when $k=1$. Here, we analyze serial
interconnections of $1$-contracting and $2$-contracting systems. We provide
conditions guaranteeing that such interconnections have a well-ordered
asymptotic behaviour, and demonstrate the theoretical results using several
examples.

Dynamical Systems