 
Summary: A kinetic mechanism inducing oscillations in simple
chemical reactions networks
J. CoatlŽeven and C. Altafini
September 10, 2009
Abstract
It is known that a kinetic reaction network in which one or more secondary sub
strates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work
is to provide a description of the functional form of such a cofactor action guaranteeing
the onset of oscillations in sufficiently simple reaction networks.
Keywords: chemical reaction networks, oscillations, Hopf bifurcations, PoincarŽeBendixson
theorem.
AMS classification: 37G15, 80A30, 92C45.
1 Introduction
Apart from circadian rhythms, many biochemical networks exhibiting oscillations have been
intensively studied, such as, for example, cell cycle [1], Ca+
induced oscillations [8], glycolysis
[15, 20, 14], yeast metabolic cycle [19], genetic oscillators [4, 18]. Given a biochemical reaction
network with nonlinear rate laws, it is in general difficult to predict exactly when oscillations
will arise, as this depends on the "graph" of the reaction network, on the form chosen for the
kinetic equations, and on the values assigned to the parameters. In this context, systems in
