Special Session 135: Dynamical Systems in Mathematical Biology: Epidemiology, Population Dynamics, and Reaction Networks

Structural Determination of Bifurcation and Multistability in Chemical Reaction Networks
Takashi Okada
Hiroshima University
Japan
Co-Author(s):    
Abstract:
In living cells, numerous reactions are interconnected through shared substrates and products, thereby forming complex reaction networks. The dynamics of such networks remain insufficiently understood, largely because the quantitative forms of reaction-rate functions are often unknown. To address this difficulty, one can adopt a structural or topological approach that does not rely on detailed kinetic assumptions or specific parameter values. Here, we present our recent studies on structural methods that enable us to determine bifurcation properties of chemical reaction systems directly from network structure, including which parameters control the onset of bifurcations and which parts of the system exhibit bifurcating behavior. We further discuss multistability, focusing in particular on a structural criterion for identifying the molecular species that should be observed to distinguish and classify coexisting steady states.