  We present a minimal model of an incompressible flow in square duct subject
to a slight curvature. Using a Poincar\'e-like section we identify stationary,
periodic, aperiodic and chaotic regimes, depending on the unique control
parameter of the problem: the Dean number (De). Aside from representing a
simple, yet rich, dynamical system the present simplified model is also
representative of the full problem, reproducing quite accurately the
bifurcation points observed in the literature. We analyse the bifurcation
diagram from De = 0 (no curvature) to De = 500, observing a periodic segment
followed by two separate chaotic regions. The phase diagram of the flow in the
periodic regime shows the presence of two symmetric steady states, the system
oscillates around these solutions following a heteroclinic cycle. In the
appendix some quantitative results are provided for validation purposes, as
well as the python code used for the numerical solution of the Navier-Stokes
equations.
