Symmetry properties and bifurcation analysis of a class of periodically forced chemical reactors

In this work, we discuss how periodic forcing may induce symmetry properties into mathematical models of chemical reactors. We define a class of reactors subjected to discontinuous periodic forcing, and show that all the reactors belonging to this class have spatio-temporal symmetry. This symmetry and its influence on the possible bifurcation scenarios are discussed. The bifurcation analysis is carried out with suitable discrete systems that exploit a property of the Poincaré map. In fact, it is shown that the spatio-temporal symmetry induced by the forcing makes the Poincaré map of the continuous system an iterate of another map. On this basis, a technique to implement parameter continuation methods is proposed. With such a technique, it is also possible to characterize symmetric and nonsymmetric regimes and unstable limit sets otherwise undetected with "bruteforce" approaches. Examples for reverseflow reactors and networks n-reactors with periodically switched feed and discharge positions are presented.