Hopf Bifurcation in Distributive Phosphorylation–Dephosphorylation Chemical Reaction Networks: Existence and Absence Results
Lorand Gabriel Parajdi, Ph.D. Lecturer, Faculty of Mathematics and Computer Science, Babeș-Bolyai University, Cluj-Napoca
March 12, 2026, 1:00 p.m.
Abstract: In this presentation, we investigate the presence and absence of Hopf bifurcations in chemical reaction networks (CRNs) derived from a distributive phosphorylation-dephosphorylation network. By examining modifications to the sequential and distributive double phosphorylation network, we identify sub-networks that either allow or preclude simple Hopf bifurcations. Using algebraic tools such as Hurwitz determinants and convex parameterization, we classify 20 isomorphism classes of reduced networks obtained through species elimination. While most reduced networks are incapable of simple Hopf bifurcations, we identify specific configurations that exhibit periodic behavior. Moreover, we identify an “atom” network responsible for these bifurcations, providing insights into the dynamical potential of CRNs and their structural properties. This work enhances our understanding of the emergence of complex dynamics in biochemical systems and is a joint collaboration with Assoc. Prof. Casian Pantea, Ph.D., from West Virginia University, USA.