This workshop is aimed at the participants in the Junior Trimester Program "Renewal Equations, PDEs and non-equilibrium systems in biological modelling". It is not possible to apply only for this workshop.
Group leaders:
- Manuel Esser
- Katharina Schuh
- Holger Spellmann
- Nicola Vassena
Description:
Reaction (or interaction) networks provide a unifying framework for modeling systems of interacting entities across a wide range of disciplines. When specified in concrete applications, the nature of the entities and their interactions varies. In chemistry, they describe chemical species and the reactions among them. In epidemiology, they represent compartmental classes and the transitions between them. In ecology, they encode trophic relations within 2 food webs or other competitive relations. In economics, they model goods that are transformed through industrial activities.
From this broad range of applications and relevance follows a wide variety of mathematical tools. Deterministic approaches are grounded in algebraic geometry and dynamical systems theory, and they address the existence and stability of equilibria, as well as non-equilibrium dynamics. Stochastic approaches include particle-based and agent based models that capture randomness, finite-population effects and emergent behaviour; they address long-time behaviour, metastability and large-deviation principles. Key questions concern the connection between interaction rules and qualitative behaviour across stochastic and deterministic descriptions.
The workshop aims at bringing together these complementary mathematical perspectives, connected by a common interest in systems of interacting entities regulated by a network structure. A main goal is to profit from different approaches to similar problems and to discover at the same time new directions and applications, with the goal of fostering dialogue between stochastic and deterministic viewpoints.