Dynamical Systems with a Network Structure

The field of network dynamical systems resembles a hydra with many heads. One prominent line of research focuses on coupled-cell networks, emphasizing symmetry, bifurcation, and normal forms. Another influential thread is reaction network theory, which adopts a more algebraic perspective centered on stoichiometry, network structure, and dynamical properties such as stability and persistence.

Despite an overlap in biochemical motivations and a shared emphasis on structured dynamical systems, these approaches have largely developed within distinct communities, with limited methodological and conceptual cross-pollination. The techniques and languages used often reflect different mathematical cultures: one grounded in dynamical systems and symmetry, the other in algebraic and combinatorial frameworks.

The overarching goal of this workshop is to explore potential connections and foster dialogue between these perspectives, to better understand the “body” of this many-headed hydra, and to uncover unifying principles that may enrich both fields, while reinforcing strong connections to realistic applications in the natural sciences. The workshop is organized around three concrete challenges: network design rules, bistability in reaction networks via a symmetry approach, and higher-order interactions in coupled-cell networks via a hypergraph structure. A combination of introductory tutorials, structured discussion sessions, and focused working groups will tackle these challenges, while also allowing for the emergence of new synergies and the foundation of long-term collaboration.

The organization of this workshop was initiated during a visit of Nicola Vassena at VU Amsterdam, supported by the Amsterdam Center for Dynamics and Computation.