Routes to Multiple Equilibria for Mass-Action Kinetic Systems

Figure 2

Two types of bifurcations leading to multistationarity. (a) Folding: multistationarity arises due to a folding of the equilibrium manifold. As it is seen in the figure, the multistability region is enclosed by two folding (or limit point) bifurcations with respect to a mass conservation constant. Importantly, the three equilibria indicated in the figure by red squares correspond to different vectors . (b) Branching: multistationarity arises via equilibrium branching; in this case the three equilibria indicated by red squares correspond to the same vector (there are three different values of for a given ).

(a)

(b)