There are fundamental challenges to understanding the dynamics of regulatory networks, a problem is central to systems biology. Biological regulatory networks are typically nonlinear multiscale systems and hence that the associated mathematical models are often characterized by heuristic nonlinearities and poorly defined parameters. Even when the parameters are well defined, their values are typically unknown. Furthermore, precise experimental time series data for these systems is not available.
To deal with these issues we propose a novel mathematically rigorous but computable approach to nonlinear dynamics based on combinatorics and algebraic topology. We refer to the output of the computations as a Database of Dynamics as it allows the user to query for specific dynamic structures. We will discuss the Database of Dynamics in the context of regulatory networks that are modeled using switching networks.