Dynamic equivalence in tangent spaces from vector fields of chemical reaction networks

Distinct chemical reaction networks (CRNs) may lead to the same dynamics; this fact has been termed the fundamental dogma of chemical kinetics. We use Lie algebra of derivations to construct a tangent space along trajectories of vector fields, induced by CRNs, such that their dynamical structure is preserved via the construction of a diffeomorphic map Φ. Thus, given two CRNs, it is possible to express the states (i.e. chemical species concentration) of one CRN as function of the other and vice versa, via the composition of their diffeomorphic maps. We call these map compositions the dynamical equivalence. ► We use Lie algebra of derivations to construct diffeomorphic maps from reaction networks. ► We propose a definition of dynamical equivalence by composing diffeomorphic maps. ► Oscillatory chemical reaction networks as a proof of concept for dynamical equivalence. ► Dynamical equivalence among chemical reaction networks following mass action kinetics or not.