  Coupled map lattices (CMLs) are prototypical dynamical systems on
networks/graphs. They exhibit complex patterns generated via the interplay of
diffusive/Laplacian coupling and nonlinear reactions modelled by a single
iterated map at each node; the maps are often taken as unimodal, e.g., logistic
or tent maps. In this letter, we propose a class of higher-order coupled
dynamical systems involving the hypergraph Laplacian, which we call hypergraph
coupled maps. By combining linearized (in-)stability analysis of synchronized
states, hypergraph spectral theory, and numerical methods, we detect robust
regions of chaotic cluster synchronization occurring in parameter space upon
varying coupling strength and the main bifurcation parameter of the unimodal
map. Furthermore, we find key differences between Laplacian and hypergraph
Laplacian coupling and detect various other classes of periodic and
quasi-periodic patterns. The results show the high complexitiy of coupled graph
maps and indicate that they might be an excellent universal model class to
understand the similarities and differences between dynamics on classical
graphs and dynamics on hypergraphs.
