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Complex systems with global interactions tend to be stable if interactionsbetween components are sufficiently homogeneous. In biological systems, whichoften have small copy numbers and interactions mediated by diffusing agents,noise and non-locality may affect stability. Here, we derive stability criteriafor spatial complex systems with local and non-local interactions from acoarse-grained field theory with multiplicative noise. We show that long-rangeinteractions give rise to a transition between regimes exhibiting giant densityfluctuations and pattern formation. This instability is suppressed bynon-reciprocity in interactions.

Long-range interactions and disorder facilitate pattern formation in spatial complex systems