Coupled hypergraph maps and chaotic cluster synchronization

Abstract 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 at each node; maps often taken as unimodal, e.g. , logistic or tent maps. In this letter, we propose class higher-order coupled involving hypergraph Laplacian, which call (CHMs). By combining linearized (in-)stability analysis synchronized states, spectral theory, numerical methods, detect robust regions chaotic cluster synchronization occurring in parameter space upon varying strength main bifurcation unimodal map. Furthermore, find key differences between Laplacian various other classes periodic quasi-periodic patterns. The results show high complexity graph indicate that they might be an excellent universal model to understand similarities dynamics classical graphs hypergraphs.