  We propose a simple model to analyze the traffic of droplets in microfluidic
``dual networks''. Such functional networks which consist of two types of
channels, namely those accessible or forbidden to droplets, often display a
complex behavior characteristic of dynamical systems. By focusing on three
recently proposed configurations, we offer an explanation for their remarkable
behavior. Additionally, the model allows us to predict the behavior in
different parameter regimes. A verification will clarify fundamental issues,
such as the network symmetry, the role of the driving conditions, and of the
occurrence of reversible behavior. The model lends itself to a fast numerical
implementation, thus can help designing devices, identifying parameter windows
where the behavior is sufficiently robust for a devices to be practically
useful, and exploring new functionalities.
