Towards a Scientific Method for Dynamical Systems

The premise of this paper is the following value proposition: Models are good when they describe a system of phenomena, and they are better when they can predict the effect of interventions upon the system. We introduce a formalism by which dynamical system models can be obtained by specifying basic constituent processes in the form of petri nets, mediated by the Law of Mass Action. We prove the universality of this procedure with respect to ordinary first order differential equations in rational functions. In addition, we introduce a simple graphical procedure for calculating dynamical systems from petri nets in our formalism, which we use to recover several well-known dynamical systems. For proof-of-concept, we use our method to obtain a differential equation model for the HES1 gene transcription network that predicts post-intervention behaviours of the network.