Chemical reactions as dynamical systems on the interval

We consider the most general chemical reaction of the typen ₁ A ₁+...+n _N A _N m ₁ B ₁+...+m _M B _M whereN,M1,n ₁,...,n _N andm ₁,...,m _M are positive integers defining the stoichiometry, andA ₁,...,A _N andB ₁,...,B _M are the names of chemicals or ions. We assume that _i=1 ^N n_i= _j=1 ^M m_j. The time evolution of the concentrations is given by the law of mass action and leads to a dynamical system (with discrete or continuous time) which is governed by a polynomial map of the interval B, C], where B0 and C1. We define the physically meaningful range for the parameters of the map, and we show that, within such a range, the map has a unique fixed point, which is stable and a global attractor, with the exception of one particular case, where bifurcation is observed.