We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are presented in the context of applied problems to visualise the strengths and drawbacks of the approach.

The major aim of capturing such a broad overview is to understand the interrelations between network theories that seem to be distant from the mathematical perspective.

A. Puchalska, M.N. Cartier van Dissel, P. Gora, M. Iskrzyński, M. Kramar Fijavž, D. Manea, A. Mauroy, I. Nakić, S. Nicaise, M.B. Paradowski, G. Rotundo, E. Sikolya, Journey Through the World of Dynamical Systems on Networks, In: M. Čolić, J. Giesselmann, J. Glück, M. Kramar Fijavž, A. Mauroy, D. Mugnolo (eds), Mathematical Models for Interacting Dynamics on Networks (MAT-DYN-NET 2024), Trends in Mathematics. Birkhäuser, Cham, (2026) 225-274.