Speaker
Description
Multistability and oscillations are ubiquitous in nature, appearing in contexts ranging from biochemical reaction networks and cellular regulation to ecological and chemical processes. These phenomena are often associated with qualitative changes in system dynamics as parameters vary, making bifurcation analysis a fundamental tool for understanding the mechanisms that generate such behaviors.
In this talk, we give an overview of the recent developments in the systematic study of local bifurcations of equilibria of small mass-action systems, including fold, cusp, Andronov-Hopf, Bautin, and Bogdanov-Takens bifurcations. The intensive study of nontrivial dynamical properties in small reaction networks is justified and motivated by recent advances in inheritance theory, a mathematical tool that allows us to lift nondegenerate behaviors from smaller networks to larger, more realistic ones.
Joint work with Murad Banaji (Lancaster University, United Kingdom) and Josef Hofbauer (University of Vienna, Austria).
