https://hal-cea.archives-ouvertes.fr/cea-01484719Luck, J. M.J. M.LuckIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueMehta, A.A.MehtaS. N. Bose National Centre for Basic SciencesUniversality in survivor distributions: Characterising the winners of competitive dynamicsHAL CCSD2015[PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech][NLIN.NLIN-AO] Nonlinear Sciences [physics]/Adaptation and Self-Organizing Systems [nlin.AO]De Laborderie, Emmanuelle2017-03-07 16:05:462023-03-24 14:53:042017-03-08 09:17:01enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-01484719/document10.1103/PhysRevE.92.052810text/html; charset=utf-81We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and non-survivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterisation is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept -- the {\it dynamical fugacity}. Remarkably, in the large-mass limit, the survival probability of a node becomes independent of network geometry, and assumes a simple form which depends only on its mass and degree.