System theory of rational positive systems for cell reaction networks

Biochemical reaction networks are in realistic cases best modeled as rational positive systems. Rational positive systems for biochemical cell reaction networks are defined as dynamic systems which are rational in the state but linear in the inputs. An academic example is provided. The positive orthant is positively or forward invariant for the differential equation of the system. Results are presented for the realizability of an input-output relation as a rational positive systems and for the form of state-space isomorphisms