  We present a general framework that enables one to model high-order
interaction among entangled dynamical systems, via hypergraphs. Several
relevant processes can be ideally traced back to the proposed scheme. We shall
here solely elaborate on the conditions that seed the spontaneous emergence of
patterns, spatially heterogeneous solutions resulting from the many-body
interaction between fundamental units. In particular we will focus, on two
relevant settings. First, we will assume long-ranged mean field interactions
between populations, and then turn to considering diffusive-like couplings. Two
applications are presented, respectively to a generalised Volterra system and
the Brusselator model.
