  Chaos and oscillations continue to capture the interest of both the
scientific and public domains. Yet despite the importance of these qualitative
features, most attempts at constructing mathematical models of such phenomena
have taken an indirect, quantitative approach, e.g. by fitting models to a
finite number of data-points. Here we develop a qualitative inference framework
that allows us to both reverse engineer and design systems exhibiting these and
other dynamical behaviours by directly specifying the desired characteristics
of the underlying dynamical attractor. This change in perspective from
quantitative to qualitative dynamics, provides fundamental and new insights
into the properties of dynamical systems.
