Competitive cluster growth on networks: complex dynamics and survival strategies

TL;DR

This paper investigates how network structure influences competitive cluster growth, revealing sensitive dependence on initial conditions and proposing strategies to manipulate cluster survival through selective networking, with universal distribution patterns guiding these strategies.

Contribution

It introduces a network-based extension of the competitive cluster growth model and develops survival strategies by analyzing the effects of selective networking with clusters of various sizes.

Findings

High sensitivity to initial configurations demonstrated by damage spreading.

Survival strategies can be devised by connecting to small or large clusters.

Universal probability distributions suggest effective winning strategies.

Abstract

We extend the study of a model of competitive cluster growth in an active medium to a basis of networks; this is done by adding nonlocal connections with probability $p$ to sites on a regular lattice, thus enabling one to interpolate between regularity and full randomness. The model on networks demonstrates high sensitivity to small changes in initial configurations, which we characterize using damage spreading. The main focus of this paper is, however, the devising of survival strategies through selective networking, to alter the the fate of an arbitrarily chosen cluster: whether this be to revive a dying cluster to life, or to make a weak survivor into a stronger one. Although such goals are typically achieved by networking with relatively small clusters, our results suggest that it ought to be possible also to network with peers and larger clusters. The main indication of this comes from the probability distributions of mass differences between survivors and their immediate neighbours, which show an astonishing universality; they suggest strategies for winning against the odds.