DSYREKI · Dynamical Systems and Reaction Kinetics Networks

The primary goal of the project is to advance the theory of dynamical systems governed by differential equations with multiple parameters, leveraging this enriched understanding to dissect mathematical models that mirror real-world phenomena and processes. Our exploration will span both qualitative and quantitative attributes of these systems, including their general structure, solution properties, bifurcations, stability etc. In a practical application of our theoretical insights and computational techniques, we will delve into the analysis of certain biochemical networks, with a focus on those integral to reaction kinetics. Employing a synergistic approach that melds symbolic and numerical computation, we aim to enhance the analysis of stability and bifurcations within intricate biochemical systems. This will be achieved by developing bespoke symbolic-numeric tools designed to uncover instances of multi-stability and bifurcations. Our qualitative and computational evaluations will serve dual purposes: elucidating established biological phenomena and forecasting emergent ones.Additionally, our research will extend to the emphasizing parameter estimation and the resolution of control dilemmas for biomedical applications. We will explore novel territories of positive and impulsive control, areas currently lightly tread in existing literature.This project is inherently interdisciplinary, seeking to fuse and expand upon the methodologies from mathematics, applied mathematics and reaction kinetics, alongside the computational algorithms of symbolic computation. Incorporating the principles of the Green Charter, our research will also emphasize sustainable practices and the development of simulations aimed at addressing and mitigating environmental impacts associated with the processes under study. Furthermore, this endeavor promises substantial training opportunities for early-stage researchers, fostering an environment conducive to learning and innovation.