Griffiths phase emerging from strong mutualistic disorder in high-dimensional interacting systems

Abstract: The majority of analysis of interacting systems is done for weak and well-balanced interactions, when in fact topology and rare event factors often result in strong and sign-biased interactions when considering real systems. We analyse the impact of strong mutualistic interactions in a uniformly weighted Erd\H{o}s-R\'enyi network under generalised Lotka-Volterra dynamics. In difference to the typical case we show the interaction topology and system dynamics combine to produce power law abundance distributions in a critical region of the phase diagram, identifiable as a Griffiths phase. We find asymptotic expressions for the fixed point solution in this region, and establish the boundary of this region as when topology alone determines the abundance distribution. We show that the Griffiths phase persists for strong mutualistic interactions more generally, and survives when combined with weak all-to-all competition.