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Boros Balázs: Deterministic mass-action systems

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Csütörtök, 13. Február 2025, 10:00 - 11:00






We start by introducing the basic concepts and terminology of Chemical Reaction Network Theory, a field of applied mathematics born in the 1970s. After presenting some classical results (e.g. the celebrated Deficiency-Zero- and Deficiency-One Theorems), we will touch upon the longstanding Global Attractor Conjecture and related questions, including persistence and permanence in mass-action systems.
Next, we detail our work on classifying the smallest bimolecular mass-action systems that admit an Andronov–Hopf or Bautin bifurcation. Then, we relax our assumption on the molecularity and investigate bimolecular-sourced, trimolecular networks: we characterize all generic bifurcations of positive equilibria in planar systems with at most four reactions.
In the last part, we will introduce the recently developed concept of inheritance. The idea is to infer dynamical behaviors in networks from subnetworks. This powerful tool helps understand emergent behavior and justifies the intensive study of small networks as motifs in larger, real-world networks.
As a bonus, if time permits, we will briefly discuss global stability, permanence, and the center problem in planar S-systems, a class of ODEs introduced in the context of biochemical systems theory.

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