Routes to Multiple Equilibria for Mass-Action Kinetic Systems

Figure 1

Example 1: a reversible chemical reaction network describing a Michaelis-Menten mechanism. The network involves five chemical species , where and represent substrate and product, respectively, transformed under the action of the enzyme via intermediates and . Each maximal set of connected complexes is a linkage class. Following the representation proposed in [28], with each linkage class we associate a reference complex (in squares) that serves to construct the stoichiometric subspace in the first place and will lead to the dynamic structure (1). Assuming mass-action law, we associate with each arrow a chemical reaction coefficient . The zero complex (complex number 3 in the graph) represents the environment which in this case exchanges substrate and product with the system.