Persistent Subspaces of Reaction-Based Dynamical Systems

Abstract

Various types of dynamical systems, such as ordinary differential equations (ODEs) or partial differential equations (PDEs), are widely applied not only in chemistry but also in many scientific disciplines to model the dynamics arising from interactions described by reactions between molecules, individuals, or species. This study provides an overview of how Chemical Organization Theory (COT) can be used to analyze such systems by identifying all potentially persistent species solely from the underlying reaction network, without the need for simulations or even knowledge of reaction constants or kinetic laws. Two minimalist examples with only three resp. four species are used to introduce all fundamental definitions including a new, naturally arising concept of persistence, and to illustrate the fore-mentioned technique without mathematical details such as proofs. Thereby, COT is shown to provide measures to analyze, compare, and construct very complex systems on an abstract level and thus to complement other powerful techniques for the analysis of complex systems such as deficiency, RAF theory, elementary modes, graph theory, Lyapunov functions, and bifurcation theory.