Modeling the dynamics of biological networks requires understanding system parameters. Typically, these parameters are high dimensional or difficult to measure which complicates this task. To further complicate matters, collecting data in real world examples may be expensive so often data is also sparse.
In this talk we will present a generally applicable combinatorial approach to studying dynamics which aims to overcome some of these issues. We will illustrate the method with some examples and describe how this approach has revealed surprising connections between dynamical systems, algebraic geometry, and order theory.