Non-reciprocal interactions enhance heterogeneity

We study a process of pattern formation for generic model species anchored to the nodes network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by directed links. By assuming system exhibit stable homogeneous equilibrium whenever only interactions are considered, we prove such can turn unstable once suitable allowed for. Stated differently propose sufficient conditions allowing patterns emerge using non-symmetric coupling, while initial perturbations about homogenous fade away reciprocal coupling. The instability, precursor emerging spatio-temporal patterns, be traced back, via linear stability analysis, complex spectrum an interaction Laplace operator. Taken together, our results pave way understanding many heterogeneous complexity found in ecological, chemical or physical systems composed interacting parts, no diffusion takes place.