Our next online seminar at the address  https://meet.google.com/bgt-oqys-gme 

Abstract: We start with a few simple mass-conserving deficiency-one mass-action systems that admit (multiple) limit cycles. With the help of the continuation software MATCONT, we visualize all the limit cycles in the different stoichiometric classes at once. Then we show that adding new chemical species into the reactions of a chemical reaction network (CRN) in such a way that the rank of the network remains unchanged preserves its capacity for multiple nondegenerate equilibria and/or periodic orbits (in fact, this is how the deficiency-one networks at the beginning of this talk are constructed). The result adds to a family of theorems that tell us which enlargements of a CRN preserve its capacity for nontrivial dynamical behaviors. It generalizes some earlier claims and complements similar claims involving the addition of reactions into CRNs. The result gives us information on how ignoring some chemical species, as is common in biochemical modeling, might affect the allowed dynamics in differential equation models of CRNs. The talk is based on https://arxiv.org/pdf/2112.06801.pdf