Bifurcations of a polynomial differential system of degree n in biochemical reactions

In this paper, we consider a polynomial differential system of degree n, which was given from a general multimolecular reaction in biochemistry as a theoretical problem of concentration kinetics. The high degree of polynomials involves so many difficulties that we hardly give coordinates of all equilibria, although that is basic for qualitative analysis. Using techniques of decomposition, truncation, and elimination with a computer algebra system, we first give qualitative properties of all equilibria, and then analyze their saddle-node bifurcation and Hopf bifurcation both for real parameters and for integer parameters.