The goal of the project is to find structural network conditions for the occurrence of zero-eigenvalue bifurcations.

The motivation is finding new efficient ways to detect multistationarity and oscillations, which are features of great importance for biochemical networks.  Multistationarity is the property of a chemical system to exhibit two or more distinct steady-states (equilibria), co-existing under otherwise identical conditions. The phenomenon has been proposed as an explanation for many epigenetic processes, including cell differentiation. Oscillations are crucial in the regulation of metabolic processes, circadian rhythms, and other important biological functions. Mathematically, both multistationarity and oscillations may appear as a consequence of bifurcation phenomena involving a zero eigenvalue of the Jacobian of the system, at an equilibrium.

More specifically, for ODEs systems arising from chemical reaction networks, this project addresses

  • Saddle-node bifurcation (simple eigenvalue zero);
  • Takens-Bogdanov bifurcation (algebraically double eigenvalue zero),

aiming at necessary and sufficient network conditions that guarantee the occurrence of such bifurcations. The ultimate goal is finding biochemically meaningful network motifs that indicate a possible bifurcation behavior and using established kinetic models to explicitly find bifurcations in relevant biochemical networks.

Project leader at IZBI: Dr. Nicola Vassena

Duration: 01.01.2023 – 31.12.2024

joint project third-party founding

Coordinator: Prof. Dr. Peter F. Stadler