Bifurcation and coexistence of several limit cycles in models of open two-variable quadratic mass-action systems

Abstract

We investigate models of open, isothermal and homogeneous chemical reaction systems with two intermediates. The assumption of mass-action kinetics leads to polynomial rate equations. We exclude the occurrence of higher than bimolecular reactions with respect to the two intermediates and thus restrict ourselves to quadratic rate equations. It is shown that nevertheless considerably complex behaviour is possible. So two-variable quadratic mass-action systems are constructed that have up to three coexisting limit cycles. Any normal bifurcation of a limit cycle that is possible in a plane system of first order differential equations is shown to occur in quadratic mass-action systems, too.