Dr. Nicola Vassena

Dr. Nicola Vassena

SCIENTIST & PROJECT LEADER

nicola.vassena@uni-leipzig.de

Room:

ACADEMIC CAREER

  • B.S. in Mathematics, Università degli Studi di Milano, 2013
  • M.S. in Mathematics, Freie Universität Berlin, 2016
  • Ph.D. in Mathematics, Freie Universität Berlin, 2020 Thesis: “Sensitivity of metabolic networks”, advisor: Bernold Fiedler
  • Postdoc at Freie Universität Berlin 2020-2022 AG Nonlinear dynamics
  • Postdoc at IZBI, Leipzig Universität 2023, Walter-Benjamin program of DFG
   

SCIENTIFIC INTERESTS

I am a mathematician interested in biological applications. I study networks of interacting populations, as biochemical networks or prey-predator systems. I focus on dynamical phenomena such as stability of equilibria, multistationarity, and the insurgence of oscillations. I try to understand the network motifs that possibly indicate such phenomena.
MAIN TOPICS
  • Biochemical and Metabolic Networks
  • Population dynamics
  • Nonlinear Dynamics
  • Bifurcation Theory
 

Project VA 1858/1-1  “Zero-eigenvalue bifurcations in Chemical Reaction Networks”

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.    

PUBLICATIONS

https://nvassena.github.io

2023 (5)

  • Alejandro López-Nieto, Phillipo Lappicy, Nicola Vassena, Hannes Stuke, Jia-Yuan Dai. Hybrid Bifurcations and Stable Periodic Coexistence for Competing Predators. arXiv preprint arXiv:2310.19604. 2023.
  • Nicola Vassena. Structural conditions for saddle-node bifurcations in chemical reaction networks. SIAM Journal on Applied Dynamical Systems. 2023. 22: 1639-1672.
  • Nicola Vassena. Structural obstruction to the simplicity of the eigenvalue zero in chemical reaction networks. Mathematical Methods in the Applied Sciences. 2023. n/a:
  • Nicola Vassena. Symbolic hunt of instabilities and bifurcations in reaction networks. Discrete and Continuous Dynamical Systems - B. 2023.
  • Nicola Vassena, Peter F Stadler. Unstable cores are the source of instability in chemical reaction networks. arXiv preprint arXiv:2308.11486. 2023.
 

MISCELLANEOUS