Universality in survivor distributions: Characterising the winners of competitive dynamics - Archive ouverte HAL Access content directly
Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2015

Universality in survivor distributions: Characterising the winners of competitive dynamics

(1) , (2)
1
2

Abstract

We 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.
Fichier principal
Vignette du fichier
1511.04340.pdf (642.02 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

cea-01484719 , version 1 (07-03-2017)

Identifiers

Cite

J. M. Luck, A. Mehta. Universality in survivor distributions: Characterising the winners of competitive dynamics. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (5), ⟨10.1103/PhysRevE.92.052810⟩. ⟨cea-01484719⟩
80 View
69 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More