  We study a system of nonlocal aggregation cross-diffusion PDEs that describe
the evolution of opinion densities on a network. The PDEs are coupled with a
system of ODEs that describe the time evolution of the agents on the network.
Firstly, we apply the Deterministic Particle Approximation (DPA) method to the
aforementioned system in order to prove the existence of solutions under
suitable assumptions on the interactions between agents. Later on, we present
an explicit model for opinion formation on an evolving network. The opinions
evolve based on both the distance between the agents on the network and the
'attitude areas,' which depend on the distance between the agents' opinions.
The position of the agents on the network evolves based on the distance between
the agents' opinions. The goal is to study radicalization, polarization, and
fragmentation of the population while changing its open-mindedness and the
radius of interaction.

Analysis of PDEs;Numerical Analysis;Numerical Analysis